BQ3050: RC6 pin of BQ8050 to output PWM abnormal

If PWM worked at one point and then stopped working, chances are that something inside the bq3050 was damaged during regular use.

Is there anything on the end user side that could cause violation of abs. max. (see table 7.1 in the datasheet)? Note that this isn't just about a specific abs. max. for a pin, e.g. MAX VREG25+0.3V for RC6 but in general.

Your schematics showing the circuits connected to RC6 look fine. There's something in your system that causes violation of one or more abs. max. values which isn't shown in these schematics.

If something like that happens, TI can sometimes perform failure analysis on a broken part. You'd have to submit the broken part to a field applications engineer and then it will take several weeks at TI to analyze what actually got damaged on the chip level.

It's really not possible to fix this for you based on the information that you provided. The schematics look ok and "it worked but then broke at the end user" has too many unknown variables to make a useful statement what caused the problem.