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Strong acid equilibrium

So a teacher at school told me that strong acids do not create an equilibrium in general, while weak acids do (thats the difference, strong acids namely ionize completely). However, I lately stumbled upon a passage reporting that when experimenting with extreme pH, so extreme concentrations of acids, strange things start to occur and strong acids are not able to ionize completely, resulting in an equilibrium. I would explain this by the extreme concentration -> less water molecules in the vicinity of acid to react -> less chance to ionize. But then I thought, are strong acids in fact not also creating an equilibrium, but because they react so strongly, they immediately release their proton. The conjugate bases are extremely weak, but they should be able to pick up a proton right? They simply become and acid, and release it immediately again. Please clarify this entire situation for me, thanks already.