The left seems to feel that any misfortune should be borne by society. The right seems to feel any misfortune should be borne by the individuals. Neither is right, the real question should be to what degree we expect people to prepare for misfortune.
I had a very similar thought the other day, although it was based around risk rather than misfortune. Both the left and the right feel compassion toward misfortune, and both want to reduce risk. But they have very different and fairly antithetical approaches to that problem. The left wants to shift risk from the population experiencing the risk onto those who are not experiencing the risk. The right wants individuals to have a say in how much risk they're willing to take on, and thinks individuals should be able to decline to take on someone else's excess risk to some degree.
Oversimplified, of course... but:
Left: Bob is at risk of losing his house, because he can't pay the mortgage. Everyone is required to pitch in $200 to help Bob out. If you don't pay in the $200, we're going to ostracize you and call you names, because you're a horrible person with no empathy and you just hate Bob you poopy-head.
Right: John is just barely making his own mortgage payment, and Roger is trying to put some money away to help with upcoming medical bills - it's not right of you to force them to pay another $200 for Bob's benefit. Bob probably lost all his money gambling and doing blow off of hooker's asses anyway, immoral bastard that he is.
Reality is pretty much that both Left and Right would prefer if Bob weren't at risk of losing his home, but disagree on how to keep that from happening, and how much of the risk is Bob's versus Everyone's.