If a tenant thinks that simply moving away from the property will cancel out the debt they owe to a landlord, they are mistaken. In the same way that a creditor such as a bank or a credit card company can pursue payment due to them, so can a landlord. Even if they have abandoned the property the landlord may take the tenant to court through the eviction process. Once the judge rules in the landlord's favor the tenant will need to leave (if they haven't done so already) and pay what is owed. That is not always as easy to collect on. The landlord may choose to pursue the debts in small claims court or even turning the account over to a collections agency. That does not necessarily mean that the landlord must go through the eviction process in order to turn a file over to a collection agency. If the tenant owes money for any reason - such as damage done to the property upon move out - they may follow this path. A landlord may also sue for the money owed tin a debt. This is meant to collect the money, not to remove the tenant from the property. Depending on local laws, if the courts issue a debt collection judgement, it can remain active for ten years or more and the creditor may even be able to garnish wages to obtain the money.
You should always be up-to-date on your local and federal laws when it comes to both the eviction process so that you do not accidentally skip a step. If you do, the judge may throw your case out even if the tenant doesn't show to defend themself. Also be aware of what your state/city laws say when it comes down to what to do with abandoned property. These laws change from place to place, and in some cases the landlord may be allowed to sell the abandoned property to cover the debts the former tenant owes to them, though this is not the case in all areas. Often when the landlord is allowed to do this there are restrictions that dictate every step of the process.