As an example, the bed bugs came from the hotels, not the homeless. NextStep did not have them till the hotels donated all of their furniture when they were "remodeling" their floors. (In a news story afterwards, it was stated that 75+% of all of the hotel rooms in Honolulu have bed bugs.)
3 Weeks after the first major hotel donation, the place was completely infested. No one bothered to tell us the dressers, mattresses and cabinets had bed bugs in them, otherwise it would have been dealt with differently. 
And yes, something was done beyond that. We spent $5,000 with the pest control people the first month to try to eradicate the problem, and a full spray of the whole facility every few weeks after. ASAIK they still do it. But once infested, the only way to get rid of them is do like the hotels did, toss out EVERYTHING and start from scratch.
After that, no homeless shelter would take hotel furniture unless it was thoroughly cleaned first before it ever was put into the facilities.