My XP did this recently, it lasted 5 days. He was enormously abusive and I’ve just got him out of the house for good, this week.
The 5 days stonewalling contributed to the last straws of the relationship. There are no “strategies” for dealing with it, as it is abhorrent behaviour and a means of control.
It is controlling because it makes you walk on eggshells and invades your mental space as you anxiously wonder what’s wrong/what you did/what he’s thinking/whether he’s enjoying it/if he knows how much it’s hurting you, and WHEN it will stop and when he will decide to make it stop. He’s punishing you and “teaching you a lesson”. It is likely you are not actually “criticising” or being tactless or a “bad communicator”, but standing up for yourself!
I am deeply familiar with this type of emotional abuse tactic, and this is what your partner is doing to you. Threats of leaving the family equates to more punishment and is certainly not a healthy way of communicating, especially with a partner who has anxiety (probably due to him).
When I was being stonewalled, I used the time to gain peace and quiet and cheerily go about my business, but that is not always advisable.
I called my local women’s aid branch frequently and got the emotional support and advice I needed -if you reach out to them, they’ll be great help. (Or vent on here, there are so many wise and caring people!).
Good luck, get insights, get Googling, get out!