Yes, stars grow by “eating” the gas and dust around it. It was thought that there was a limit as to the size to which a star could grow but it has been found that this is not true. The logic behind this is that when the star grew large enough and ignited it blew away the gas and dust around it and reached its maximum size. The study found that after the star’s ignition there’s still gas and dust for it to feed on continuously. Not only do they “eat” gas and dust but also if they’re big enough then their gravity pulls smaller stars towards it and absorbs them. This makes them even bigger.
To find out more check out the ScienceNOW article by Phil Berardelli.