If the inverted pyramid is in an "old-fashioned" economy and society, where the great majority of adults generally work hard until the last few years of their lives, and families mostly do their own service work, then the inverted pyramid might not be a serious problem.
But if you're hoping for something closer to the modern, Western ideal - education until age ~25, work until age ~60, retirement until age ~90 - then the inverted pyramid is going to need at least one of:
(1) Armies of imported service workers - to staff all the nursing homes, retirement homes, cruise ships, restaurants, etc. that the huge "top" of that pyramid need / want.
(2) Armies of robots so advanced that they can fill the great majority of those jobs. WithOUT requiring an extra army of humans to build, pay for, maintain, run, etc. those service worker robots.
(3) Huge changes in medical technology and social expectations, so that most of those service workers are never needed.