How long was it a rental?
The basis of the property is listed when the property becomes a rental.
Depreciation starts on the property when it becomes a rental and is depreciated over 27.5 years.
Depreciation does not stop when the property is "Idle" only when it is retired from service.
When you sell the property, unless you sell for less than the remaining value, you'll have a gain and/or depreciation recapture.
So if the property was purchased for 100,000 and depreciated down to 60,000, anything over 60,000 up to 100,000 is depreciation recapture and anything over 100,000 is a gain.
Depreciation is taxed at income rate, gain is taxed as Capital Gain.
If you try to add to the basis now, you'll need to add the additional depreciation for that additional basis when you report the sale. That most likely means additional depreciation recapture.
According to the IRS:
"Retired From Service
You stop depreciating property when you retire it from service, even if you haven’t fully recovered its cost or other basis. You retire property from service when you permanently withdraw it from use in a trade or business or from use in the production of income because of any of the following events.
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You sell or exchange the property.
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You convert the property to personal use.
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You abandon the property.
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The property is destroyed."
Pub 527
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