Slides back and forth or rotates?

if rotates, then there's an adjustment you can do on the cable length.
a couple of inches near the throttle, is an adjuster.
loosen the lock nut and rotate the long nut to lengthen the cable and take up the slack.

Is it the entire control assembly that is sliding, the throttle tube, or the grip itself?

If it's the control assembly you can see if the phillips head screws on the back of the housing are loose. They don't need to be oh-my-god tight, just a bit beyond snug.

If it is the throttle tube, it could be that the previous owner installed an aftermarket unit (universal) that is too narrow for the slide. Do note that there should be about 1/16-3/32 of side-to-side play.

If it is the grip itself you can squirt some hair spray under the grip. Attach a red wand to the spray can.

Mine does the same, but I don't think the bar end cap is what holds the throttle tube on, does it?  I have my bar end caps off for Winter b/c I made struts that go from the mirror stems to the bar ends to keep the handlebar muffs from pushing on the brake/clutch levers.  With the caps off, the throttle tube stays put.

You don't need a
Surprise!
Engine off
Hands on handlebars
Lean and pull back
Not trying to break anything, easy,just figure out if the throttle is gonna pop out and change your input on the steering.
Prove what you think you know. Finding out the handlebars aren't as solid and dependendable as you thought they were could be bad.