No, it doesn't work that way unless you are having a cost segregation done.
Normally, when property is purchased and placed into service as a rental, the basis is split between building and land only.
The building depreciates, the land does not.
If later you add to the rental, such as an appliance, that appliance is entered as a new asset for the rental and starts to be depreciated on its own based on it's basis (cost value).
When the rental is sold, if there is remaining value to the additional asset, the sale's proceeds will be split between land, building and the additional assets remaining on the books.
It is possible for a "Cost Segregation" to be done where assets, such as appliances, are valued and listed separately. This is usually done if there is machinery involved, but it can be done for residential rentals as well. There isn't much value in doing it for the average rental, but if that is the direction you want to go, I suggest you hire a professional to make the adjustments.
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