This will depend on your state laws.
It might be helpful to know that an equitable remedy (eviction) is distinct from a money judgment. Sometimes these are handled in two different courts or two different proceedings within a court. If you get the eviction, you might not get the money judgment or vice-versa.
I think we customarily ask for a no-trespassing order in conjunction with the eviction, which won’t stop them from coming on the property but gives you ammunition when you call the police to report it.
If you get a money judgment, I believe it is customary for the judgment to include all “future” rent due until the judgment is satisfied (or the home leaves).
Once you get a judgment, you will have to “execute” the judgment as a separate step. Depending on your state laws, it may or may not be simple to attach a lien to the home, but just because you have the lien does not end the saga. Once you have the lien you have to enforce payment, and there’s nothing to stop someone from moving or trashing the home despite your lien unless you are vigilant.
Don’t expect your deadbeat tenant to care about your legal rights, and don’t expect mobile home movers to look out for your interests. Once the home is hooked up and gone, what do they care?
Once you get the eviction, if the home is not moved out you should expect it to be abandoned and you’ll have to go through your state’s process/procedure for that. It might be simpler to buy them out and save yourself the hassle. (Wait until post-judgment though).