Does submitting a request for an installment agreement legally ‘fix’ the taxpayer’s liability owed or can the liability later be argued?

The tax liability can be “argued” or more appropriately collected upon as long as the statute of limitations on collection (10 years for the IRS) is still open. If the amount of the installment payment is less than necessary to full-pay the liability over the collection statute (known as claiming “hardship”), the IRS will most like revisit the taxpayer’s ability to pay via a collection information

Installment Agreements

Installment Agreements

statement every 1-2 years.

If on the other hand, an Offer in Compromise is accepted and the taxpayer remains in compliance for 5 years following the offer, the liability is considered paid in full.
The are a few exceptions to these rules including a collateral agreement in which the taxpayer may have to pay more if they have the potential to earn substantially more and meet certain