miners will be paid only by transactions right? So what if then the time comes that the btc price fell down? Is that possible?
That has a low chance of happening as price increases as demand increases(most of the times)
As to your question, you'll be dead by then . From what I heard from DannyHamilton and other members, the year the last BTC(partial) will be mined is 2140*. So yeah, lot of time for that to happen. Anyway coming back to what will happen, miners will just get the tx fees, and hopefully by then either BTC price is very high that mining is still sustainable or transaction fees increase. The former is more likely I believe.
*Googled and it seems , its just an estimate but you get the idea.
** Forgot another possiblity that is, (majority of) nodes decide that number of bitcoins should be increased, so the protocol may be changed