If you choose not to substitute yourself in as a party, how do you imagine that you would be able to enforce the order? Walk into the Sheriff's Department, ask for the enforcement of an order of eviction, and hope that they don't ask who you are?

When you own a property, you may evict the tenants. If you don't own a property, you have no standing to evict the tenants. You won't find a statute in any state that specifically describes what happens when a property is sold after an order of eviction is issued but before the eviction is completed.