I am someone who cannot throw out a plant; not as long as there is one green fiber hanging on to life in its wizened stem. The philodendron currently cascading down the end table in my living room is, in fact, a refugee from the basement where my mother had intended to euthanize it; one day while fetching something from the freezer I noticed one sad little yellowed nubbin emerging from the dead vine, then brought the pot upstairs, watered the potbound dirt and waited to see what would happen. And the plant came back; a small resurrection that I found cheering.
This fall I overwintered my fancy-leaved geraniums -- let the frost nip the leaves, then cut the plants down almost to the soil, then let them sprout new growth over the winter in my sunny kitchen window. Right now they're pale and spindly, and look like they won't amount to anything, but I know that they will when it gets warm enough around here to put them back outside.
Here is the story of another rescued geranium.