Are homeless people more likely to commit crimes?
While I cannot answer the question of whether homeless people are more likely to commit crimes it does appear that if a person has less to lose by being a criminal than they have to gain then they may pursue that option.

Homelessness is like a gateway drug, it leads to many unwanted situations, some of which maybe incriminating depending on the threshold of the person in question, and the harshness situation being faced.
However i will say homeless people are more susceptible to commit crimes

For example

Sex in exchange for accommodation is a way out of homelessness

Does the risk of being homeless motivate "hard work"?
Yes, one for fear of being homeless and everything that comes with it, and two, in search for and of a better life, meanwhile, if otherwise, the person in question feels already dejected or lost or has given up!