And that can be a problem ... but, that sort of event is rare. For the most part, addresses of fugitives are verified by more than the subject's say-so, it is most often accompanied by documentation as a result of a conviction and supervised release (probation or parole), or, a residence as indicated on a driver's license or ID card. However, if he is arrested and gives the address of a friend or other family member - as was likely the case with LdiJ's situation - that can open the door to problems because the address is unverified. Yet, there is almost always a reason the address was provided - usually because a sympathetic ear lives or lived at the location so it was a safe address to provide. Plus, there is an incentive for people in custody to give a physical address - it can support their release. Transient individuals may not be permitted a release on a promise to appear or pending further action, but, with an address they can.
Typically, the police are not going to waste their time returning to an empty nest. They will either get weary of the time taken (or their supervisors will), or, they will get wind that he is somewhere else. When they have little or nothing else to go on, they may continue to revisit any possible locations until he is found. We have a fellow in my town who lives on-and-off with his mother and we are constantly going to her place and searching for him. She says he's not there and doesn't live there, yet he is frequently sighted at night, and one of his sister's has seen him there frequently. So, we keep going back because we know that mom is covering for him.
And so it goes ...
