Does basis remain in Traditional IRA after a complete conversion?

If you convert your entire Traditional IRA to Roth IRA, but the amount you convert (the value of the Traditional IRA at the time you convert) is less than the basis (after-tax amount) in the Traditional IRA, does that leave a non-zero basis in the Traditional IRA after you convert, even though there is no money there? And can that basis be used later, e.g. if you later make a deductible contribution to your Traditional IRA, can part of it be considered after-tax due to the basis left over from before?

A situation where this might arise is where you are doing a "backdoor Roth IRA contribution", which involves making a non-deductible contribution to Traditional IRA, and then converting that to Roth IRA. But suppose that the IRA lost money in between the contribution and the conversion, so that the amount you converted to Roth IRA (even though you converted your entire Traditional IRA) is less than your non-deductible contribution to Traditional IRA.

The amount of the non-deductible contribution becomes the "basis" (after-tax amount) in the Traditional IRA, and this basis does not change when the value of your IRA goes up or down. When you convert to Roth IRA, it reduces the basis, but since the amount converted is less than the basis, it seems that some basis would be left over, even though the value of the Traditional IRA is 0. For example, if you made a $5500 non-deductible Traditional IRA contribution, and the IRA lost money to$5000, then you converted that entire $5000 to Roth IRA, it seems that you would be left with$500 of basis in your Traditional IRA.

This seems counter-intuitive, but I can't find any rule that would remove your remaining basis if you take out the entire Traditional IRA. And a look at the forms seems to agree that there should be left-over basis. For example, assuming a $5500 non-deductible contribution and a$5000 conversion, your Form 8606 Part I would look like this:

1. 5500
2. 0
3. 5500
4. 0
5. 5500
6. 0
7. 0
8. 5000
9. 5000
10. 1.000
11. 5000
12. 0
13. 5000
14. 500 <- this is your basis left for future years (on a future year's line 2)


I can't find any form instruction that would cause you not to carry over that \$500 of basis onto future years.