Before worrying about strength of fingers check out your hand proportions.
Everyones' hands are different in squareness of palm, lengths of fingers and shape of finger tips. The amount of flesh on your fingertip and the length of your nails will affect the shapes of the three fingers used in Thumb Position and the ease of playing thumb position
In the "ideal hand" (which incidentally suits every instrument except French Horn?) the palm is broad and square, the pinkie extends past the last joint of the 3rd finger and the index finger is shorter than the 3rd finger.
Even so the finger tips need to be fleshy enough that you are not pressing the strings down with your fingernails in Thumb Position. The above hand shape enables you to align your fingers nicely when they turn and point diagonally towards the bridge as you go into Thumb Position and higher. The fingers are arched but the index finger is more bent and the 3rd finger is straighter. The end of your index finger comes down vertically and the string groove is diagonally across the top flesh. This is where the shape of the end of your finger and the length of (even cut very short) fingernail are important.
Have you ever played snooker/pool/billiards? Your left hand forms a bridge with curved fingers, and fingertips rest on the table in order to support the cue. The weight of your arm rests on your fingertips. The same principle can be used for Thumb Position. The three fingertips and the thumb form a line that is dictated by the string. If the fingers are arched they can "hook" the strings down, back towards your body, not "press" them down.
The only reason your fingers might have to collapse their last joint is if your nails project too close to the end of your fingers. Yes, this does put you at risk of injury. Can that last joint then be strengthened sufficiently by exercise so that you can play with flatter but not collapsing fingers to stay on the flesh?
To generally strengthen your hand and fingers I suggest finding a soft foam "stress ball", that you can close your hand entirely around with your pinkie closing towards the thumb. I have found balls that have a range of softness. Don't start too hard! Another thing I do is exercise each finger by curling it against pressure from my other thumb. Maintaining good finger shapes as you play will gradually strengthen them naturally as you play anyway.
DP