What do you call a 'usury' ('bad deal') agreement that doesn't involve a loan?

I'd go with exploitative:

exploitative:

making use of a situation or treating others unfairly in order to gain an advantage or benefit.

"an exploitative form of labor"

(Oxford)

Drops in precisely in your template (after a swap from "a" to "an"):

He signed an exploitative work agreement because he had been unemployed for a year and was desperate and hungry.

It's similar in meaning to "extortionate", but it's more specific to your case of exploiting a situation, rather than "extortionate", which involves creating the situation through force or threats. You didn't impoverish the person in question, you just took advantage of their desperation.

I would call this a predatory work agreement although I don't think there's a specific term (excepting the legal term that 66974) posted.

I think usury is very specific to charging interest on loans so the thing you are talking about isn't related to it at all really. That's why I read this question, I was wondering what possible type of situation might exist that could be called usury but didn't involve a loan of money or goods.

extortionate work agreement

from

extortion

the act of getting something, especially money, by force or threats:

-Collins

From your original post...

...you agree to do be contracted out at low rates but you have to pay most your income to a middleman.

He signed an extortionate work agreement because he had been unemployed for a year and was desperate and hungry.

The "middlemen" often withhold passports, provide sub-standard housing, and confiscate most of the earnings of the victim. Those who try to escape this type of toxic life-style are usually threatened with violence, or (often worse) denunciation to the immigration services.

This is a form of human trafficking.

Human trafficking involves the use of force, fraud, or coercion to obtain some type of labor or commercial sex act. Every year, millions of men, women, and children are trafficked worldwide – including right here in the United States. It can happen in any community and victims can be any age, race, gender, or nationality. Traffickers might use violence, manipulation, or false promises of well-paying jobs or romantic relationships to lure victims into trafficking situations. [Emphasis mine]

Read more...-US Department of Homeland Services

The "agreement" they signed may have no legal bearing.

It is illegal anywhere. If you find yourself a victim of this kind of treatment you need to find legal counsel now. If you know of someone in this situation you need to take action, now.

You started your question with the concept of usury, which is generally illegal; see e.g. 2010 New York Code 5-501, which has the heading Rate of interest; usury forbidden. Therefore, I will provide a legal term for a contract that is so unfair as to be illegal—or, rather, unenforceable.

The legal term that seems appropriate is unconscionable. It doesn't specifically refer to 'work usury', but to any contract where one side is trying to take advantage of another, weaker side.

Discussion

Black's Law Dictionary gives the following definition:

unconscionable agreement  An agreement that no promisor with any sense, and not under a delusion, would make, and that no honest and fair promisee would accept. - Also termed uncon­scionable contract; unconscionable bargain.

For what it's worth, here is Wikipedia's take on it:

Unconscionability (sometimes known as unconscionable dealing/conduct in Australia) is a doctrine in contract law that describes terms that are so extremely unjust, or overwhelmingly one-sided in favor of the party who has the superior bargaining power, that they are contrary to good conscience. Typically, an unconscionable contract is held to be unenforceable because no reasonable or informed person would otherwise agree to it. The perpetrator of the conduct is not allowed to benefit, because the consideration offered is lacking, or is so obviously inadequate, that to enforce the contract would be unfair to the party seeking to escape the contract.

And here is a relevant segment from notes on contract law from NYU law school:

d. Unconscionability

i. Williams v. Walker-Thomas Furniture Co. I – (D.C., 1964) - π purchase items on an installment plan. The contracts were designed with a cross-collateralization clause so that the amount due spread over all items purchase – keeping an open balance on everything until all items were paid for. The π claimed she did not understand the contracts, but signed them anyway. She claimed there was no (1) meeting of the minds, and (2) the contracts were against public policy. The court found for the defendant.

1. This was a unilateral mistake on the part of the π.
2. The contracts may have been deplorable, but were not against public policy.
3. One who refrains from reading a contract and in conscious ignorance of its terms voluntarily assents thereto will not be relieved from a bad bargain.
4. Duty to read, or have someone read it to them.

ii. Williams v. Walker-Thomas Furniture Co. II – (US Ct. App DC Cir. 1965) – appeal from above case. The court of appeals found that the district court did have the power to declare an unconscionable contract.

1. Unconscionability is generally recognized to include an absence of meaningful choice on the part of one of the parties together with contract terms that are unreasonably favorable to the other party.
2. Whether a meaningful choice was present can only be determined by consideration of the circumstances surrounding the transaction.
3. The test to be applied is whether the terms are “so extreme as to appear unconscionable according to the mores and business practices of the time and place”.
4. Dissent – the π knew where she stood. J. Danahar is concerned that if this contract is declared unconscionable, it could be problematic for others who need to purchase items on installment plans.
5. Court relied on UCC [Uniform Commercial Code] as persuasive authority.
6. Procedural Unconscionability = how the contract was made (absence of meaningful choice, or gross inequity of bargaining power)
7. Substantive Unconscionability = the terms of the contract (terms that are unreasonably favorable to one party).

In legal contexts that would be referred to as a “leonine agreement:”

leonine:

A leonine treaty or convention is one that is forced upon a weaker state by a stronger one. In some jurisdictions the adjective is applied to contracts which are manifestly unfair.

(OxfordReference)