Perseverance

Perseverance is the Purple Soul that fell into the Underground, which was captured by Asgore. The human with this soul was possibly armed with a notebook, that Frisk now finds torn and partially broken. This soul was conserved by Asgore to be used when destroying the Barrier, but the mission failed since Determination wasn't captured canonically. Perseverance is also the soul used in Muffet 's battle, where she transforms Frisk's soul into purple with cups of "tea". When in battle, Perseverance is seen only being able to move up and down on purple lines, which are actually webs in Muffet's fight.

Trivia

 * The Torn Notebook is possibly ruined by the pass of time, since it is estimated that a long time passed since the last human fell.
 * This is also kinda confirmed as Toriel says that "Frisk is the first human to fall in a long time", suggesting a lot of time, maybe years, had passed.