There are an absolutely exorbitant amount of factors and variables involved in your question and answer...I could talk for hours.
But I will be simple.
Invariably strength goes up and down when cutting... Some of the main variables include: water balance, glycogen, % change in LBM, and energy level. However there are more.
Cutting is a means to an end. Going from point A to point Z.
My best advice is to leave the strength ego before you start cutting. Unless you are a performance athlete, powerlifter, or ego-maniac... strength in lifting weights is no big deal.
Sure your strength may temporarily go down... As long as you aren't losing LBM, it will come back. And it is possible to maintain strength while cutting. But, again there are many variables.
The most important thing to maintaining strength long term, is to make sure you aren't losing LBM. That's it.
You find what works for you. Cutting/Dieting is a series of ups and downs, and you have to get over it. The ups and downs are physiological, physical, and mental. It's part of the game.
But as a general rule to maintain LBM while calorie restricted, you need to lift heavy. And you need to make sure you don't over train.
Many people approach a cut with the idea that they have to amp up the workouts, lift with high reps and high volume... And they assume they must to metabolic workouts at high intensity and high frequency (meaning increasing the amount of days lifting.) This just isn't the case.
Lift in the realm of heavy. If you want to add metabolic type workouts in there... There is nothing wrong with that, but just make sure that is done at a reasonable volume and frequency and always after heavy lifting is complete. For instance 3 sets in the 6-8 rep range followed by 3-4 sets in the 10-12 maybe to 15 range. You could even go a bit lower in rep range.
You just want to make sure you do lift heavy and don't overtrain... that's the idea in the most simplest form...
Like I said before, there are a myriad of variables to take into consideration... but you have to start somewhere