Do the TV cable lines belong to the tenant of the property or to the cable company?

Generally, any utility service owns and maintains the service up to a specific take off point. For things like water & sewer, it is normally at the street where it connects to a main. For cable it is normally at the connection point outside the house. After that, they are owned and maintained by the property owner.

That last point is important to your question. As any improvements that are done and become integral to the property, like cable, wires, systems....things that are attached and custom to the property, by a non commercial tenant (residential)...first: are normally under the lease are only allowed to be done with permission of the owner (at which point the right to remove - if any - and obligation to restore the property are agreed). Second, if not done by agreement they become part of the property as a leasehold improvement. Normally, upon termination of the lease, the owner can agree to keep them as improvements (like painting a wall without permission), or charge for removing them and restoring the property.

They are not the tenants.

You should check your lease/agreement for your circumstance. Probably found under the area addressing tenant improvements or maintenance.