How do I retrieve files from my iPhone 4 after apps started crashing?

The iPhone 4 has a 32-bit processor, and cannot update past iOS 7.*. I would not be surprised to find that it cannot access the App Store any more, or that third-party app developers have moved on. I don't know why your apps are crashing, but at this late date, I would think the chances of getting help from app developers to fix this problem are slim and none.

Note that if you have filled up the storage on the iPhone, that could lead to crashes, and removing some files to free up some space might help.

If storage isn't full, you need to ask yourself, what else might have changed, that would be likely to affect a large number of apps?

One possibility that comes to mind is some sort of hardware failure – including, say, the battery wearing out and needing to be replaced. The old version of iOS that runs on that phone might not have the same sort of battery management / performance throttling that modern versions of iOS use to try to avoid or reduce crashes when a battery can no longer consistently provide enough power for peak workloads.

If you notice the crashes happening especially often with apps that might require more electrical power (games that are doing a lot of graphics work), that might suggest a worn out battery, especially if your battery health is below 80% (I don't know if old versions of iOS display it), the battery has never been replaced, or it has been a very long time since the last battery replacement.

A_Mu wrote:

Thank you for your response. I wanted to clarify that I am not interested in updating iOS or any apps, as I believe that such updates may not even be possible in the App Store anymore. I’m actually content using the apps and games in their current versions without any updates.

Regarding storage, I assure you that my device storage isn't full or anywhere near that.

Retrieving the files is only one part of the problem, the main issue I’m experiencing is that these apps and games keep crashing, and I’d really like to get back to using them as I did a few months ago.

If you have any suggestions on how to resolve this problem, I would be grateful.

That device became obsolete years ago. Apple no longer supports it. In the case of software problems, deleting and re-installing the apps and/or erasing and restoring the device are the most effective way of solving the problem...

Unfortunately, either one is going to leave you with a device with no data and no 3rd party apps at all.

It's time to let it go and move on.