The sentence 'she involved herself' is correct and usable in written English.
You can use it when describing an action that someone took on their own, without relying on another person or outside help. For example, "Jane was passionate about helping out her community, so she involved herself in various volunteer activities."
"I think Lynn put herself in the situation so that she involved herself in the business side of things".
The word no was not in her vocabulary, and as a result she involved herself in every team priority.
She involved herself deeply in her sons' schools, was an active member of Achievement Rewards for College Sciences (ARCS), and was a champion for special education programs.
On her return to New York she involved herself more deeply in Zionist activities, becoming secretary of the Federation of American Zionists in 1910.
Ms. Sterne believed that every record she produced should have a purpose, and she involved herself with everything, from the packaging to the liner notes.
Hewlett-Packard's chairwoman, Ms. Dunn, has acknowledged that she authorized the internal inquiry, and documents have shown that she involved herself in it.
Clearly, she involves herself deeply in the words she sings.
Then she involves herself, with willed innocence, in someone else's adulterous mess, and malicious gossip does the rest.
When a student named Jesse Oxfeld wrote a column for The Stanford Daily about press coverage of Chelsea, his editor fired him for violating the paper's rather precious policy of not commenting on Chelsea unless "she involves herself in a newsworthy event at Stanford".
She advises everyone to focus on things outside themselves, explaining that she involves herself in activities that directly or indirectly benefit people.
She involves herself in relationships in which the parties involved take responsibility for their behaviours and consider each person's feelings, needs and desires.
