In 1644, Li Zicheng made an offer to the Chongzhen Emperor would fight the Qing dynasty and eradicate all other rebels on behalf of the Ming, if the Ming dynasty would recognize Li Zicheng's control over his Shaanxi-Shanxi fief, pay him 1 million taels and confirm Li Zicheng's noble rank of Prince. Li Zicheng did not intend to overthrow the Ming Emperor or kill him.
Pretty sure that by 1644, when the Ming imperial court's direct control north of the Yangtze was severely limited to plainlands around Shuntian + Shandong and Hebei, this supposed offer was not a sincere one, nor would it be abided by the Shun court (which was established on January 1st of 1644). The source for this supposed offer was from a 19th century work by a lone court official who supposedly had access to classified Imperial documents, but it's not seen elsewhere. If we were to trust that it happened, many do believe the offer was done to humiliate Chongzhen, who had previously maintained a staunch stance of refusing to view the peasants as anything more than upstart rebels (previous negotiations involved giving money and having them stand down and return to peasant, but never becoming an independent fief with a rank of a prince, which would've been ludicrous to the Emperor who viewed them as mere peasants).
Also the Shun army's situation would not permit this offer to actually go through.
1) Li Zicheng had no reason to believe the Ming would survive any on-slaught by him, the last vestiges of a well-equipped army was still in Shanhai Pass, those in Datong and other Garrisons were not taken seriously by either the Shun or the Manchus. There's no reason to give up all of Henan/Hebei for just Shaanxi/Shanxi when the Ming no longer posed a serious enough threat. Plus Li Zicheng did not consider the Manchus a serious enough threat at that point, allowing Wu Sangui to be antagonized easily. The Shun army was still under the impression that their army was powerful enough to withstand any campaign by the Manchus - proven desperately wrong later.
2) None of Li Zicheng's generals would have allowed the offer to happen. They were at the gates of the Imperial city, and despite how ravaged it is, in their mind it's still rich beyond what they have seen. Their morale up to this point was simply supported by the idea that once they conqueror Beijing, their beloved general would firmly establish himself as the Son of Heaven and they would be richly rewarded (in both land and plunder). To have an almost 200,000 army retreat when they're one gate away from this happening would just be asking for a rebellion, especially when the rebels did not have the best track record in discipline. And as we can see, soon after conquering Beijing, the Shun army integrity rapidly disintegrated after 1) preoccupied in plundering the city and lost further motivation to fight 2) disillusioned when they did not receive land grants as promised as many of them were peasants who lost land 3) asked to retreat back West rapidly hence did not even have all the time to enjoy their plunder.
Also finally, the Ming did give many peasant leaders offers of surrender provided they return to their land of origin and returned as faithful peasants, but those like Li and Zhang repeatedly rebelled as soon as the money given by the imperial treasury ran out and the army had to leave to fight the Manchus.
Princess Gao to assure her son's immediate succession and fall of the Ming, or the Dali Lama.
Dali Lama?? Hopefully you're not serious.
And to have Lady-General Gao Guiying (now, Princess Gao) give birth to the heir to the throne - a royal Prince always needs an heir
It's suspected that Li Zicheng was rendered impotent at some point thru his military career, he had several wives and concubine but none were pregnant in his later years, especially the ones when he had ample time to lay low. He however, had his nephew and younger brother available as heir.
