I've had my PS box start moving on me on two different occasions, caused by both things being discussed here, so I can tell you what I saw with both issues.

When the welds broke on the steering box bracket:
This happened about 10 years ago as I was leaving home. When that happened, I didn't completely lose my steering, but it was close - the car pretty much went whatever way it wanted to. I was able to get it back into my driveway, popped the hood, and moved the steering wheel through the open window (with the motor off) while I watched what was happening to the steering box. When I moved the steering wheel, the box would move an inch or so in either direction, and it was also moving upwards an inch or so - it was easy to tell something was broken, as the box was moving all over the place. An inspection showed that the welds had broken between the K frame and the steering box bracket, and re-welding the bracket fixed the issue.

When the steering box bolts loosened up:
This happened 2 summers ago. I noticed some slop in the steering, and it was gradually getting worse. Again, I popped the hood and moved the steering wheel while watching what was happening to the steering box. This time, the box moved a much smaller amount - only maybe 1/4 inch each way, and just a little upwards also. I could tell this time that something was still holding the box in place, but it was loose. I found that both bolts had loosened up, so I cleaned them up and installed with a little locktite, and the slop in the steering went away.