It happens regularly. The most notable 'tidy' example I can think of would be when the Governments of US and Canada 'bailed out' General Motors. They did exactly what I'm talking about; they created a new legal entity called NGMCO Inc. which purchased almost all the Assets of the 'old' GM, including trademarks, names, websites, etc.

The key here is that the selling company was bankrupt. In such a case, the creditors want to try to get money back out of their 'investment' so the asset sale is done to cover debts. Selling liabilities generally doesn't raise money for those creditors, so often after the money is all sucked out, whatever remaining liabilities exist are functionally void. Legally they remain until the corporation is dissolved, but with no ability to act on the liabilities (ie., no money to pay) this doesn't functionally matter.

The 'old' GM changed it's name to 'Motors Liquidation Company' and retained the liabilities. Shareholders of the 'old' GM were left holding the bag, so to speak. Technically, it was further split into trusts to 'handle' liabilities, but realistically 'old' GM sputtered out holding liabilities while 'new' GM carried on with minimal penalty.

You can have less 'tidy' cases as well, where substantial parts of a company are sold in an asset sale/purchase but leave behind a working company. In those cases the liabilities are not functionally abandoned. Disney purchasing FOX, for example.

Further reading:

https://www.investopedia.com/terms/a/asset-sales.asp

https://www.reuters.com/article/oldgm-exit-idUSN3121109620110331/?feedType=RSS&feedName=cyclicalConsumerGoodsSector&rpc=43

https://en.wikipedia.org/wiki/General_Motors_Chapter_11_reorganization

https://en.m.wikipedia.org/wiki/Acquisition_of_21st_Century_Fox_by_Disney