I’ve done a fair bit of analysis of this situation, so here’s my two cents.
The gap between the two sides here is considerable, and unlikely to be bridged. The PRC holds virtually all of the cards and could resolve it by leverage. HK being a series of islands and a peninsula that only shares a common border with the mainland, it is easily cut off; it cannot sustain itself. Even this, to say nothing of the use of hard force, would result in repercussions globally that the PRC would prefer to avoid. They are very cognizant of appearances and have worked to paint the protesters as the guilty party throughout the disturbances.
The PRC does not need HK nearly as much as it did in the past. The growth of the mainland economy in recent decades has shrunk the percentage that HK contributes to GDP. This means that the CCP leadership can afford to let HK bear the brunt of whatever happens without suffering much themselves, provided they don’t act rashly and draw sanctions from the West. A source close to Xi (as quoted in the Economist) suggests that CCP policy is “no bloodshed, no compromises” - this points to an attritional strategy, one which may take a while to resolve.
The upheaval has already cost HK considerably. Tourism is down close to 40%, and given that 80% of its tourism comes from the mainland, this will only continue to decline while the demonstrations continue. A recent Goldman Sachs estimate suggests that USD 4bn has already moved out of HK to Singapore. How long HK’s economy can remain above the threshold of acceptability for a majority of its citizens is an open question.
The 1997 handover was supposed to lead to a fifty year period of “one country, two systems,” after which presumably HK would be fully incorporated into the PRC. While it is certainly arguable that China has not upheld its end of the bargain, no one who was paying attention (including Chris Patten, the last governor of HK when it was a UK dependency) really expected them to. It was an unenforceable agreement from day one in any case.
As far as possible outcomes, the protesters have few choices, and all of them are bad. China wants this over, but they also realize that the costs of ending it quickly are potentially very high. Both sides are playing for time, but the protesters are ill-equipped to do so; their only real tool is global public opinion, and maintaining the media spotlight is not easy. Even if they escalate their activities, chances are the PRC will stand off and wait rather than respond to the provocation, knowing that a Pyrrhic victory is about all they can hope to achieve in the streets. The one thing China most assuredly will not do is allow anything that looks like independence, or even backsliding away from the One-China Principle that underlies their policies.