Yes, many of them do. You don't hear about it because most large companies have multiple divisions, some of which are still profitable. So instead of closing down the company entirely, they shutter the unprofitable parts and return the capital to investors in the form of increased dividends and/or share buybacks.
A good example is IBM. IBM recognized 10-15 years ago that most of its commodity hardware was uncompetitive. Personal computers, x86 servers, semiconductor foundry, etc. were all money-losers for IBM over the last few years. So IBM, recognizing that these businesses were failing, shut them down and sold off the remaining assets. Then they used the capital to buy back something like $30 billion in stock, and they quintupled their dividend. In effect they did exactly what you suggested for the failing portions of their business, but kept open the profitable divisions, mostly consulting and rent-seeking.
A more extreme example but less well known example of this phenomenon is Pitney Bowes. For the most part PB manufactured postage meters and some other office equipment. Recognizing in about 2007 that physical postage meters were not exactly a hot area of business, PB began paying out enormous dividends while scaling down their operations (including selling their HQ and moving to a much smaller office). As of 2016, they have liquidated about two thirds of their business compared to 10 years ago.
Strangely, Slashdotters often tend to be very scornful when tech companies do this kind of thing. I see no end of complaint every time IBM liquidates any of their businesses, no matter how small.