I will usually lose a few pounds off the 1RM's if I do a severe cut, for example 30-40% below maintenance. I am in the middle of a slow cut now (15% under), intermittent days only. Doing this, I can slowly lower BF% and actually make mild gains. My usual 4-6 month plan is to cycle between 2 weeks of higher carb/calorie powerlifting at higher reps, then 2 weeks of lower cals with only strength maintenance lifting of many fewer reps.
So no, one cannot add strength at 30% below BMR unless serious lifting is a new thing for their body. It's just reality. Cycles of strength then cut, patience and execution of the routine is everything
"They now look to a single and splendid government of an aristocracy, founded on banking institutions, and moneyed incorporations under the guise and cloak of their favored branches of manufactures, commerce and navigation, riding and ruling over the plundered ploughman and beggared yeomanry." - Thomas Jefferson, 1826