A word to describe a person who, finding themself in a bad situation, always manages to scrape by?

Solution 1:

a 'born survivor' (It's two words but that's just how the expression is)

A person who copes well with difficulties in their life:
she is a born survivor
Oxford Dictionaries

Example

She had suffered enough pain and loss for several lives, and she was a born survivor. She was strong beyond reckoning. Legion By Steven Carlton

Solution 2:

I don't think you need two words to describe this kind of person (i.e. "born survivor" or "accidental survivor").

I think the good old plain survivor works just fine:

a person regarded as resilient or courageous enough to be able to overcome hardship, misfortune, etc.

(http://www.collinsdictionary.com/dictionary/american/survivor)

Example:

Don't worry about Kurt. The odds are against him, but he'll be fine, he's a survivor.

Solution 3:

You may refer to a resilient person.

Definition: able to become strong, healthy, or successful again after something bad happens.

However, this expression is mostly used in the following sense that doesn't really convey the idea of surviving:

Resilience comes from being in control of oneself which enables a strong and robust attitude to be formed towards challenging events and poor behaviour of others. The more robust the attitude, the less impact adverse events has on individuals.