Fixing a toilet flush glitch; it's probably that stretchy-thingy

It's probably that "stretchy-thingy"!

Well, my daughter just called me to tell me the toilet in her apartment was not working like it should. She said the flush handle seemed to go far past where it used to go before it began flushing, and the flushing did not seem to have the force it should have.

"Ok, sweetheart, it isn't as bad as you might think" (I hoped). "Can you take your phone into the bathroom so I can walk you through something?"

"I guess so, hang on...ok, what?" she puzzled. "Remove the toilet tank cover", I told her. "Ok, done", she reported. "Now, look at where the flush handle goes through the tank, and check to see that the big nut inside the tank is tight", I instructed. "Yeah, it's tight; I can't turn it", she replied. "Ok, now look at the arm that goes from the flush handle out into the tank", I said (trying to visualize it in my head as I spoke). "Yep, and...?" she queried. "At the end of that arm should be a chain or strap or string or something attached...what do you see", I pried. "I see one of those thingies that looks like it tightens when it's pulled on", she described. "You mean like a wire-tie?" I quizzed. "Thank you", she exclaimed.
"Ok, see if you can tighten up on that strap so the flushing will begin when it is supposed to", I told her. "Ok, I pulled it up quite a bit", she replied, flushing as she spoke. "Yeah, it's better now", she said. "I think it's back to normal...but why would that get out of whack anyway?" she wondered aloud. "I'm not sure, really", I answered honestly. "I guess something might have stretched or something...we'll have a look next time we're over there", I added.

"Ok, thanks!" she said. "You're welcome!" I replied.

"There! I solved that one in short order and by remote control", I proudly thought to myself.

"Aha! Not so fast!" another internal voice broke in. "You know full well that stretched thingy is probably not really stretched but probably something is detached down below or something like that". "Hmmmmm.....I think you might be right about that! Well, we're supposed to go see her tomorrow, so I'll have a look then", I quietly responded, (to whom, I don't know).

Follow up:
We did visit my daughter the following day, and I investigated further into the toilet flushing glitch. It became clearly obvious to me that the tank flapper and its component parts (the "stretched thingy", the flapper itself, the attachment device which holds the flapper on the fill tube, etc.) are certainly due for upgrade, as they show signs of age and other "wear and tear". For now, though, they appear to be functioning as they should be. Time to let the landlord know so he can arrange to have it repaired or replaced.