What lesser charges might apply if Burglary can't be proven?

Hi,

This is a purely hypothetical question from a fiction writer pondering a dilemma. I can't seem to find a clear cut answer from what I've read and I'm interested to know how this scenario might pan out:

Someone enters a property they believe to be empty with the intention of sleeping there for the night. The have no intention to steal or damage anything, hurt anyone or stay indefinitely.

The property is not empty and they are caught, inside the property, by police.

My assumption is they would be arrested on suspicion of burglary, but if the police couldn't prove or argue the intent to steal or commit a serious crime, what would happen?

Would they be released without charge, would it be down graded to trespass, or something else?
I feel like it would still be illegal to have entered the property but not sure what they would be charged with.
Would it be likely they would be charged with burglary anyway?

How would intent be proved if they were caught in the property? Would it hinge on prior convictions?

Thanks for offering your time to consider my question.