If it is physically attached, it becomes part of the structure and property of the owner.   Removal of the "owner's" property by a tenant can be a theft without the owner's permission to take it. 

I have enough issues with tenants without worrying about any personal things they take with them, but if the installation does any damage to the home then I do charge them for the repairs.

But if selling the property then it should be made clear to the buyers that these things do belong to the renter and probably will not be going with the home.

It DEPENDS. 

Since a tenant is involved, that changes the entire discussion.  The answer is now "talk to your landlord."

It depends on the situation.

Great question - looking forward to your answer!

It depends.

On the lease.

On the tenant.

On the landlord.

On the state.

On the law.

On how many times this question will be asked.

Legal question. Depends on the lease.

Always a matter of debate when an item of personal property becomes a fixture.

Go by the terms of the contract.

if the tenant installed it, it can be removed, but must be disclosed.

There is a method to determine whether it stays or can go. You'll come across this in your studies and it will be on the test too

First of all, a tenant shouldn't be "installing" anything without the written permission of the landlord.   Move out remedy should be clearly stated in the agreement.  

the key is installed. that word installed. the law varies from state to state. not only can it belong not to the tenant now, but they may  be charged to take it out