I'm afraid I must disagree with Raymott here. There is nothing remotely ungrammatical about the sentence, as illustrated by the following:
A man came to me asking for a job every day for a week. In the end, I employed the man, whose left leg was hurt (although I never felt able to ask asked him how the injury had occurred).
Naturally, if we wished to distinguish the man in question from other men in terms of his injured leg, then the more appropriate sentence would be
I employed the man whose left leg was hurt.
but that does not in any way render the alternative ungrammatical!