Not going into deeper details, the process involves Ascension and Descension of the Soul.
In reality, both processes are choices made by Soul and there is nothing like “forced” to live.
Descension is a stage when a Soul who is in union with the Supreme Soul wishes to experience that it exists and experience it in variety of forms and flavors.
Ascension is a stage when a Soul decides to go back to the place where it came from, that is, to achieve the union with Supreme soul.
Between two phases, the Soul takes various forms of plants, animals, humans, ethereal beings, angels, gods etc. and experience “All That Is”.
When a Soul leaves a body/form, just before that it decides upon the next form or body it wants to take. Or it could make a choice to go back and unite with the Supreme Soul again.
However, the problem is, it has no control over the choices it makes. That is, in human form, it almost always identifies itself with mind/body. Mind being not in proper control, makes thousands of resolutions everyday and forces the Soul (who identifies itself with Mind) to obey its orders and do (or don’t) whatever it says.
At the time when Soul leaves the body, it makes a resolution whatever may be the conditioning of the Mind at the last moment and that decides its next form. That could be a lower state but in rare cases can also be a choice to reunite with Supreme Soul.
A Yogi will not depend on the choices made by Mind and will try to stop identifying itself with it, witnessing it and having it in perfect control so that an appropriate choice can be made at the time of death.
Advanced yogis will go a step further and this lets them decide even their timing of birth and other events and experiences in their life.
This is a simplified version of my understanding of the reincarnation theory from various sources.