Hi Zach,
A simple oscillator has its drive uncontrolled. An oscillator oscillates continuousy because it has gain (amplification) and positive feedback. It takes some of its output back to its input, amplifies it, gives that larger signal back to its input, amplifies it even more, etc. It can't amplify more when its transistor "hits the supply rails" when it is saturated (turned-on hard) for a half-cycle and cutoff (not conducting) for the other half cycle. Its output is the largest when the saturation and cutoff timing are symmetrical. Bias for the transistor's base (with 4.7K it is saturated most of the time, with 27K it is more symmetrical) determines its output symmetry.
However, your oscillator has a tuned LC network as its load, so its collector voltage can actually exceed the supply voltage when the transistor is cutoff. Just like a child on a swing. Give a little push (the transistor conducts a small amount) and the swing swings like a pendulum (the tuned LC network also swings) until it is back at the position that you pushed it. Give it another little push and it swings higher. The tuned LC network does too. If the transistor is an RF one with a high gain at FM frequencies, it could be operated in "class-C" where it is cutoff most of the time but has a very large output. Your transistor is a "general-purpose" audio transistor that has hardly any gain at FM frequencies so it can't take advantage of operating in class-C.