It looks like Arm is seen by regulators as being too important to not be neutral and this rules out it being bought by another chip company and almost every major chip company is now an Arm licensee, one way or another.
Arm's current owners, Softbank, wanted to sell Arm when it was under pressure from some expensive, high-profile deal failures, At the time, Softbank needed to raise cash or at least convince their own investors that they had the ability to do so. However, now they don’t need to and have benefited strongly from the technology stock market bull run over the last two years.
It has made some big bets on the market and these have paid off, so the company is now in a much better financial position. Keeping Arm makes some sense.
Arm needs to make some big investments to fund future R&D needs, but it could raise sufficient funds on its own to do this.
What Softbank might do is an IPO of at least a minority stake of Arm which was what Softbank was doing when Nvidia started snuffling around. However, at the time Softbank was worried the public markets would have likely valued Arm less than what Softbank hoped (or possibly even what they paid for it) and far less than what Nvidia offered.
Arm is likely to attract a much higher valuation because semis are hot now in a way they have not been for a long time so we expect this to be the way forward. It has the advantage that Softbank stays in charge but does not lose face.
It also means that the UK government does not have to step in and save the company from nasty foreigners.