Domestic violence cycles and escalates. If a woman's husband is violent, he will often become incrementally more violent as time goes on. (Why Doesn't She Just Leave?) The general advice in these circumstances is to get out before it escalates (and put up with being called "irrational" and "overreacting").
If a wife decides to escape a violent husband, the Islamic way requires satisfying a (probably all-male) Islamic authority of some kind (e.g. through khula). In doing so, she risks provoking further violence and being branded a rebellious wife; the authority will strive for "reconciliation" with the violent husband (see this question), sending her back into the lion's den after the lion has been angered.
There seems alternative ways out, e.g. running away, going to the police, or responding violently, although each of these can be inhibited by the husband, and could make things worse.
However, it seems that divorce by apostasy offers a plausible (and efficient) means of escape:
However, if a wife apostates from Islam, her marriage contract becomes void by her apostasy. Nonetheless, in our view, her marriage depends on her waiting period, meaning that if she re-embraces Islam before the expiry of her waiting period, then the marriage is still valid, otherwise no -- IslamWeb (another example is Darul Uloom Trinidad & Tobago)
Let's assume she doesn't genuinely disbelieve, but she fears for her safety as a result of her husband's violence, and she's invoking Qur'an 16:106 (being forced to do so, while being secure in her faith).
Question: Could divorce by feigning apostasy be used to escape a violent husband?
I'm wondering if this could work in reality.
I recognize that apostasy is punishable by death, but it's rare in most places:
In "recent decades" before 2006, the United States Commission on International Religious Freedom listed four cases of execution for apostasy in the Muslim world. -- Wikipedia