The liganding species just goes back into solution.
It's 'unbound' the same way any chemical reaction is reversed, through thermal fluctuations.
If something binds strongly enough, it may never come unbound.
In many scenarios, you'll have a situation where some reaction occurs elsewhere which causes the bound state to rise in energy relative the unbound one.
It depends on the receptor and ligand. In some cases, the binding is not strong and easily reversed. The ligand will bind and release over and over, and you'd need a high concentration of ligand to be effective. In other cases, the ligand binds and isn't released until after the ligand-receptor complex is internalized and either split up by an enzymatic reaction that allows the receptor to be recycled, or the whole ligand-receptor complex is metabolized.
A colleague of mine helped me understand binding and unbinding this way:
Binding is a two-body problem- a chemical reaction A + B -> C, with a rate constant that depends on the concentration of both A and B.
Unbinding is a one-body problem, and can be thought of as equivalent to radioactive decay. The rate constant only depends on one object, and the binding rate constant may be different than the unbinding rate constant.
ah i see so is that what biological half-lives are? i've heard the term, but i thought they were talking about the radioactive isotopes you ingest before scans