No. You don't deduct from income any amount left in your HSA and you don't add it as payment to the IRS.
You claim the deduction when you make the contribution. You can claim a tax deduction for contributions you, or someone other than your employer, make to your HSA.
Contributions to your HSA made by your employer (including contributions made through a cafeteria plan) may be excluded from your gross income and it is reported on your W-2 Box 12 code W.
The unused amount of HSA can rollover indefinitely from year to year.
Distributions from HSAs that are not used for qualified medical expenses are subject to income tax and an additional 20% tax.
For more information check: irs.gov