Is “troop” unique among English words in meaning both a group and an individual member of that kind of group?

The term "troop" can mean a group of soldiers, or it can mean an individual soldier (perhaps in this usage it was originally short for "trooper").

In fact, in modern usage, the plural "troops" almost always refers, not to multiple groups, but to multiple individuals. "Obama's surge sent 30,000 more troops to Afghanistan" means 30,000 soldiers, not 30,000 troop-sized groups of soldiers.

Are there any other nouns like that in English, where it can refer to either a group or an individual member of that kind of group? I'd be especially interested in hearing of examples where the plural form of the noun almost always refers to individuals (not groups) in modern usage.

"The canon" can mean the body of works accepted as canonical by a group; "a canon" can mean one precept of a group; and "the canons" can mean the collection of all precepts which a group follows. In some cases, "the canon" will be the same as "the canons" of a given group, if all of their canonical works concern their canons. Of course, for many groups which have a canon, their canon is a greater collective body of works which do not solely concern their canons. But I think it's similar in usage to your "troop" example.

To answer this question directly: synecdoche is a very common figure of speech:

noun

A figure of speech in which a part is made to represent the whole or vice versa

To most of us, the individual soldier (the daughter, husband, sister or father) is exceedingly more important than the rest of the troop! I perceive very conversation about the troops as a conversation about my brother.

A mother might legitimately say to her only child:

You are my brood!

A pastor might legitimately say to one of his parishioners:

Right now, you are my flock!

The rest of this answer bears more upon the flawed premise of the question. The phenomenon is actually a specialized usage of the plural form of troop with no real analogy in the singular. The plural troops can refer to a group of soldiers synecdochically in terms of its plural number:

noun

1 (troops) Soldiers or armed forces:

ODO, emphasis mine

This plural usage is common in news reports of troop deployments and movements, as in this Washington Post article:

On Jan. 10, 2007, President George W. Bush announced a dramatic shift in U.S. strategy with the deployment of 30,000 additional troops to Iraq.

Timeline: The Iraq Surge, Before and After, emphasis mine

This plural usage can create the impression that the singular troop might refer to a single soldier, because the expression 30,000 troops does, in fact, refer to 30,000 soldiers.

Also, some general expressions create the same impression with a plural usage:

"Support our Troops!"

This expression is clearly understood to mean: Support our soldiers! The analogy between the plural troops and the plural soldiers in this specialized usage generates the pseudo-impression of a potential singular usage. Although there may be rare misapplication, the singular troop is not routinely used to refer to a single soldier.

The singular troop is almost exclusively used to refer to a group:

2.0 A cavalry unit commanded by a captain.

2.1 A unit of artillery and armored formation.

2.2 A group of three or more Scout patrols.

3.0 A group of people or animals of a particular kind:
a troop of musicians

ODO

Particularly in military parlance, the plural troops does not refer to soldiers, but rather to a specific number of groups of soldiers, as seen in Remarks on the Organization of the Corps of Artillery in the British Service:

... the Corps appears to have consisted of ten Effective Battalions, one Invalid Battalion, fourteen troops of Horse Artillery, including two attached to the Rocket Service; and of twelve troops of Artillery Drivers; and to have amounted to 26,023 men, including 727 officers.

Emphasis mine

When the Random House Dictionary defines troop as "a single soldier", it is actually documenting the pseudo-impression caused by the specialized plural usage of troops:

5. a single soldier, police officer, etc.:
   Three troops were killed today by a roadside bomb.

Dictionary.com, emphasis mine

This irregular documentation, in a less-than-prestigious dictionary, could eventually lead to a sad transforming trend, but in the singular, the expression would still be soldier or trooper, rather than troop. The singular troop does not actually reference an individual member of that kind of group, but the plural troops can reference the number of individuals in the group as a synecdoche.