Yes, the problem is that even by fixing what you perceive to be a problem here, you've not accomplished much when it comes to clearing up the meaning of the sentence. It appears what you have in mind, (or whoever generated what you refer to as "the text"), is appositional. The fact that that's not automatically clear is a big problem. If the idea is that the term "a shorthand label" is referring back appositively to the term "social exclusion", then the sentence should start out,
"The Unit describes the term social exclusion as..."
Then everything form that point forward should be offset in quotes or, at minimum, italics. So the resulting construction would read,
The Unit describes the term social exclusion as "a shorthand label for what can happen when individuals or areas suffer from a combination of linked problems".
From there, in my opinion, it's just a matter of deciding whether the word defines is more suitable than the word describes. But really only the context of "the text" can provide a lead on that. However, given these parameters, I see no need for the term "a shorthand label" whatsoever.
Granted the flexibility I already addressed, suffice to say I'd opt for the following,
The Unit defines the term social exclusion as what can happen when individuals or areas suffer from a combination of linked problems.
[If it is not intended that the term "a shorthand label" function appositively with respect to the term "social exclusion", the whole meaning of the sentence is lost, leaving the reader to assume that it must mean something it does not.]
And finally, there's the matter of said definition. For starters, and for a number of reasons, I doubt it's a direct quote. It's too problematic to have been written the way it's presented, and thus, not exactly quoteworthy. First of all, it's not so much what can happen as it is what does and, more to the point, does without exception. So merely the word "happens" covers that ground unaided by the helping verb. And since only people, not areas, can experience social exclusion, it's much clearer and more accurate to say "individuals or groups of individuals" or, even more concisely, "individuals or groups".
So far, then, this leaves,
The Unit defines the term social exclusion as what happens when individuals or groups suffer from a combination of linked problems.
However, since an individual cannot alone experience that which is linked, what's really intended is simply "members of a group".
The Unit defines the term social exclusion as what happens when members of a group suffer from a combination of linked problems.
Now all the reader has to do is attempt to comprehend what the term "a combination of linked problems" means or, that is, what it's intended to mean by its author. That it can mean more than one thing is the problem. And, as always, it is the writer's responsibility to choose language which leaves as little room for guesswork as possible. But there's a bigger problem than that. No matter how you tweak the term, at the end of it all it's still a perfectly lousy definition of social exclusion. That itself, of course, may be the point you're ultimately intending to convey.
For example, our nation is a group. Our nation as a whole currently wrestles with serious economic concerns. Each member of the group is affected in negative ways. It's a shared problem with a variety of contributing factors. So here's a clear example whereby members of a group suffer from a combination of linked or interrelated problems. But it's not social exclusion.