Stars can (but don’t necessarily) have a family of planets surrounding them. Planets can (but don’t necessarily) have moons surrounding them. What about the so-called ‘failed stars’? Do they have anything as a family?
Jupiter is sometimes called a failed star. If it had just a bit more mass, fusion could start, goes the argument. Well, not really. It would take 13 Jupiters combined to have enough mass to reach the minimum needed for a brown dwarf, AKA failed star. Also, Jupiter was created within the disk of dust that surrounded our infant sun, which is how planets are made, not stars. Not even failed stars. So we can’t take any clues from Jupiter about the possibility of planets around dwarf stars.
Okay, so exactly what is a failed star? A close apparent brown-dwarf-type object to Earth is SIMP0136. It lies 21 light-years away and is 13 times the mass of Jupiter. Theoretically, it could be a brown dwarf. Brown dwarves form like other stars, but fail to get big enough. They may have some fusion of deuterium for a relatively short time inside them, but it doesn’t last. Any light they produce tends to be in the red and infrared spectrums, so despite being called brown dwarves, they would probably appear magenta or possibly red-orange. And the older the brown dwarf is, the more it cools and contracts, until it can seem to be just another planet. Scientists have recently decided SIMP0136 is just a planet, after all. A rogue planet, big enough and close enough for them to study its weather patterns.
It could have gone the other way. The size of brown dwarves range from a minimum of 13 Jupiter masses to a maximum of 80 Jupiter masses. If it managed to gather more than 80X Jupiter’s mass, it would have made it to actual stardom.
Because brown dwarves are a type of star, at least some of them do have a family of planets, such as 2M1207b and MOA-2007-BLG-192Lb. This makes sense, because brown dwarves form the same way as other stars, just in the middle of a smaller dust cloud. Once the center of the cloud collapses into a proto-brown-dwarf, the remainder of the cloud thins into a rotating disk of dust, which would normally form planets. It is thought that this disk would not extend far, since the entire cloud was small to begin with, so any resulting planets would be fairly close to the brown dwarf. It is also believed that these planets would be rocky, like Earth and Mars, rather than gas giants like Jupiter, because most of the gas would be taken by the brown dwarf. So, let's look at some known brown dwarf systems:
170 light years from Earth, planet 2M1207b orbits a brown dwarf. Its mass is somewhere between 3X and 10X that of Jupiter, and it orbits its primary at approximately the same distance as Pluto from our sun. Although there is some indication of water, it is not likely to be habitable.
Occasionally shortened to MOA-192 b, MOA-2007-BLG-192Lb is about 3,000 light-years away. This small planet is 3.3X Earth’s mass, and circles a small brown dwarf in an orbit approximately 2/3 the size of Earth’s orbit around the sun. It is believed to have lots of ice and gases, more like Neptune than Earth.
And then there’s the quadruplets: a small brown dwarf (2MASS J04414489+2301513, with a mass 20X that of Jupiter) has a companion (5X to 10X the mass of Jupiter) that could be either a planet or a sub-brown dwarf. There are also two other brown dwarves in close association. All four objects together only have 26% the mass of our sun, making it the quad system with the least mass. It is 470 light years away.
So yes, it is entirely possible - almost probable - that ‘failed stars’ will have planets. Or possibly siblings, as in the quad system.