Yes. You can reimburse medical expenses from the HSA that were incurred after the account was open. Suppose you opened the account in 2019, and you have no funds as of 2021. You deposit new funds in 2022. If you had medical expenses in 2021, you could take that 2022 money right back out tax-free to reimburse yourself. If you closed the account and opened it again in 2022, you could not do that.
Of course, your HSA bank may not want to keep an account open with no funds. You may need to leave a small balance. (After I quit my first employer, the HSA charged me $3 a month to keep the account open. Since I am not eligible to make new tax deductible contributions, I would need to leave a couple hundred dollars in the account to pay the fee, if I wanted to keep it open.)
