A resignation made under duress is invalid under Canon Law. Benedict was under a death threat and the SWIFT system had been shut down in Vatican City as an extra lever to exert pressure. The day after Benedict made an announcement about resignation the SWIFT system for the Vatican was turned back on. There is more than this but there is significant evidence that neither did Benedict resign of unencumbered free will nor did he intend to fully resign the office of the Vicar of Christ but that he intended to "enlarge the office" to be a two-person role having an active and a contemplative/passive member which isn't possible.
Apostolic succession or rather ordination as pope or as priest doesn't necessarily mean service until death. Pope Celestine V decreed in the 13th century popes are allowed to step down. Of course one is ordained priest and is in essence priest for life, just as people are baptised for life (in the view of the Church), but one can be 'in rest' or not active.
https://www.smithsonianmag.com/smart-news/in-the-entire-hist...
The assertions that pope Benedict's decision is not a free decision is not true. A foreign hostile takeover is suggested without evidence. Bank payments were suspended briefly as the Vatican was not yet conforming to European standards that came into effect.
https://www.bbc.com/news/world-europe-20903443
"After having repeatedly examined my conscience before God, I have come to the certainty that my strengths, due to an advanced age, are no longer suited to an adequate exercise of the Petrine ministry. I am well aware that this ministry, due to its essential spiritual nature, must be carried out not only with words and deeds, but no less with prayer and suffering. However, in today’s world, subject to so many rapid changes and shaken by questions of deep relevance for the life of faith, in order to govern the barque of Saint Peter and proclaim the Gospel, both strength of mind and body are necessary, strength which in the last few months, has deteriorated in me to the extent that I have had to recognize my incapacity to adequately fulfill the ministry entrusted to me. For this reason, and well aware of the seriousness of this act, with full freedom I declare that I renounce the ministry of Bishop of Rome, Successor of Saint Peter, entrusted to me by the Cardinals on 19 April 2005, in such a way, that as from 28 February 2013, at 20:00 hours, the See of Rome, the See of Saint Peter, will be vacant and a Conclave to elect the new Supreme Pontiff will have to be convoked by those whose competence it is."
There is no evidence that he has significant influence on the decisions pope Francis makes any other then that pope Francis tries to honor catholic tradition, including the views of previous popes, theologians and the past and current sensus fidei.