Assalamu Aalaikum! it is said that Allah SWT does not burden anyone more than he can bear. My question is why some people go into chronic psychological illnesses after getting struck by some incident. Doesn't this means he's been gone through the burden that he could not bear?
Alaikumassalam wa rahmatullah,
The more accurate translation of that is that “God does not hold a person responsible for more than what is in their power.” It is not about what kind of stress God allows to happen to someone, it is about what God holds us responsible for. For example if someone is unable to pray due to mental illness, God will not hold them responsible, because God only holds humans responsible for what is in their power.
God allows this universe to function in a natural way, meaning that He allows whatever that could go wrong to go wrong, although He sometimes does intervene to protect certain individuals, or to make history go a certain way He wants.
For more on why God has designed things this way see my essay: Why God Allows Evil to Exist, and Why Bad Things Happen to Good People