If the government finds out about Alice's existence, it would be afraid of the implications and possibilities especially if it is possible that there are more like Alice out there (who may not be as nice or as good as she is).
Alice willingly volunteers for tests, but the government refuses, saying she's more useful as a superhero than as a labrat.
Alice is a career labrat, her money comes from taking bribes from drug companies/the government so they can do human testing on her. Her most recent round of tests was a Super Serum or enhancment surgery.
Subverted: It turns out the government agents are perfectly rational individuals, who only want to do non-intrusive experiments, with Alice's permission, and will compensate her for her time and trouble.
Double Subverted: Those claims were lies; once she lets her guard down, the syringes come out.
Alice stays "captured" only long enough to demonstrate that her powers make her immune to the testing methods.
Zig Zagged: The government has an interest in doing this, but only tries it with a few isolated cases where they think no one will notice the super is gone; other supers are asked to voluntarily take non-invasive tests, and a few supers are never bothered by the government at all due to popularity or being too powerful to contain.
Averted: Nobody attempts to experiment on a superhero without their permission.
Enforced: The story is about an escaped experiment in the first place; it'd be silly if the lab didn't want them back for further examination.
Lampshaded: "Trying to make a lab rat out of a superhero?"
Invoked: A villain pushes the government into trying to dissect Alice, to drive a wedge between them.
Exploited: Alice allows herself to be captured for testing because she wants access to something in the base the agents take her to, and she knows she can escape their custody at anytime.
Upon gaining her super powers, one of the first things Alice does is go straight up to the president and inform him, in no uncertain terms, that if any government agents try to dissect her, she will kill them... and him.
The Agents sent to research Alice specifically treat her with kid gloves because she can't be replaced. At worst, they might keep her locked up, but anything invasive is out of the question, as it risks damaging the test subject.
"Put that scalpel down, You Fool!. Put her in the MRI, that's what it's there for; so we don't have to chop anyone open."
Discussed: "I don't think we should go public with what we can do. There are unscrupulous people who'd do anything to learn how our secret powers work."
Conversed: "I think Alice is being unduly paranoid on Generic SF Adventure Show; her power to change hair color at will probably won't get the government after her for vivisection purposes."
The attempts of the government agents to experiment on Alice are her Start of Darkness. She butchers the agents, and swears to bring down the government they represent, killing anyone who stands in her way.
The source of Alice's power is external to her, such as a magical curse, and no matter how many powered people the government vivisects, the scientists will never be able to duplicate it.
Reconstructed: The government sending agents to experiment on Alice is already dystopian, and deserves their fate.