Ah! Thank you. That does - wait - I was about to agree that that does answer the question - but: while it takes care of the preposition matter (on/in), this is a case of "their" being used in the singular:   "no ONE is left in their rack": so the question remains re: the plural - would it be "the men are not left in their rack" or "the men are not left in their racks"? I'm thinking "racks" is more likely. I'll take a look at those articles you so kindly referenced; maybe I'll find an example.