Ever since the communist revolution in China, Taiwan aka the Republic Of China (ROC) has maintained that they are the rightful government of mainland China. The People's Republic of China (PRC), controlled by the Chinese Communist Party (CCP), however, has actual possession of mainland China. Making the question irrelevant as to which government is the rightful government. This is especially challenging for the ROC, since their greatest ally, the USA, officially recognizes the PRC as the official government of China.
It seems unlikely that the Government in Taiwan will ever be able to reassert control over the mainland again, even if for some reason the CCP and PRC lose their grip on power.
Nonetheless, the ROC maintains their claim, but in recent years the PRC has increased their pressure on ROC by employing as much soft power as possible and threatening the use of hard power if the ROC declares independence. The PRC have shifted numerous diplomatic allies away from ROC, further isolating them within the international community.
The ROC is now in a position where they will continue to lose international support, becoming even further isolated and economically weakened. Alternatively, if the ROC declare themselves an independent nation, apart from China, they may enjoy greater international support and acceptance into the UN, but this move creates a whole host of other issues. Chief among them, being the PRC's explicit threat of invasion if ROC declares independence.
Not to mention, if they do declare independence and the PRC does not invade, who knows if it would even change anything for the ROC with respect to their relations with other nations.
Exiled Chinese billionaire Guo Wengui, claims that the CCP's hold on power is highly tenuous and will be lost entirely if they fail to limit the negative effects of an economic recession / depression within China.
Assuming the ROC declares independence and the PRC is unable to invade, would that mean the ROC is relinquishing their claim over mainland China?
Hypothetically, lets suppose:
the ROC currently has a legitimate claim to the mainland, and
the CCP loses power due to an economic downturn and a subsequent civilian uprising.
Could the ROC later legally assert their claim if they decide today to declare themselves an independent nation?