What is the galaxy M87 doing these days? The massive elliptical galaxy M87 in the Virgo cluster is 53,490,000 light years away. It also contains one of the largest, heaviest supermassive black holes in the known Universe. But it's also my understanding that the stellar population of this galaxy is mostly old, red supergiants. Is there any evidence for new star formation in M87? If there isn't, what is the fate of this galaxy and what is it like in modern times? That may be impossible to know for sure but what I wonder is if the remaining stars and matter in the galaxy have been swallowed up by central black hole which may be thousands of lightyears across by now.
The answer to your question is relatively straightforward: Not much. I'll delve into it in two parts: Star formation and the activity of the supermassive black hole at the center.
Star formation
M87 home to many Population II stars. They have little hydrogen and helium in them, and the clouds of gas and dust in the galaxy don't have much, either. In fact, many dust clouds can be destroyed by the intense radiation emitted by the accretion disk of the central black hole. This combines to make it seem unlikely that there will be much star formation in the galaxy.
That said, just because a galaxy doesn't have a lot of materials for star formation doesn't mean it can't form lots of new stars - at least, no under certain special circumstances. Galaxy collisions can induce high rates of star formation - starburst galaxies are good examples of this. While M87 might not be at a high risk for a collision, there is still the possibility of one. M84 is nearby, and may have had an encounter with M87 in the past. While it is a long shot (and M84 has a low star-forming rate), an interaction with the two could spawn new stars.
The supermassive black hole
You seemed particularly interested in the black hole at M87's center. It is a supermassive black hole, with a mass billions of times that of the Sun. Quite a monster, by many standards. Yet it is not doomed to swallow the galaxy whole anytime soon. It is sucking in gas and dust at a rate of $\sim10^{-1}M_{\odot}$ each year (see Di Matteo et al. (2002)) - and there are trillions of solar masses of gas, dust, and stars in the galaxy. For comparison, Sagittarius A* accretes matter at a rate of between $\sim10^{-8}M_{\odot}$ and $\sim10^{-4}M_{\odot}$ per year, depending on the exact model (see e.g. Quataert et al. (1999) and Shcherbakov et al. (2012). Still, the supermassive black hole in M87 couldn't accrete all of the matter in the galaxy in the age of the universe, if it continued at this rate.
In summary: Star formation in M87 is at a low rate, and while a galactic interaction could create a new wave of star formation, it is unlikely. The central black hole is sucking in lots of gas and dust, but it will take billions upon billions of years before it eats up a substantial amount of matter.