Since they weren't married in 2011, the IRS 2011 demand is about his unfiled 2011 obligation for his 2011 income, not hers. (But now his behavior may be endangering the main asset (house), even though you say it's in her name).
Innocent Spouse Relief may not be applicable for his (premarital) unpaid 2011 liability, and is tactically not the issue: it may not get her off the hook for the IRS placing a lien on the house for his unpaid 2011 taxes. This is not so much an issue of who the IRS believes is responsible for his unpaid 2011 tax liability, but a tactical issue about (possibly) preventing a tax lien being placed on the house (unlikely, assuming he has no other major assets), and (more likely) how to sell it with a tax lien on it and define in the Marital Separation Agreement who owes who what, who owes IRS back taxes for 2011, how much of them receives from the sale (knowing the IRS will likely place a lien on it for his 2011 liability, and the proceeds could be stuck in an escrow account for a while), who pays which taxes.
The MSA should be written knowing that financially irresponsible people often bankrupt or threaten to tactically bankrupt out of this sort of situation, to leverage concessions, and a paper promise from him to pay isn't worth much. Obviously she should try to decouple herself from him financially as fast as possible in every way possible: credit cards, bank accounts, loans, mortgages, CC balances, equity lines, insurance policies, car title, any other assets etc. Also, obviously it's in her interest to push for a status-only ruling converting her to Single by end of 2019 (for FY 2019 filing); this can be done without resolving the division of assets and debts. Run her credit report regularly, close down any shared financial doings, separate her finances.
Obviously, she needs her own separate lawyer advising on drafting a well-worded MSA, with an eye to preventing him bankrupting out or further damaging her credit until they're disentangled. A family lawyer who knows about bankruptcy and personal finances could be useful. But she also needs to move quickly and take action to take control of her finances; this will need more than a slow and lengthy exchange of legal correspondence. It's in his interest to drag things out.
(Presumably she is already trying to invoke Innocent Spouse Relief for their 2012-2018 taxes. But again, this may well not prevent the IRS placing a lien on the house).