'unbreakable commitment' is correct and commonly used in written English.
It is used to express the idea that a commitment is strong enough that it cannot be broken. For example, "They had an unbreakable commitment to each other, even in the face of adversity".
"The security of his people was always Arik's unwavering mission - an unbreakable commitment to the future of Jews, whether 30 years or 300 years from now," Biden said.
It's a market that is measured in trillions, is filled with companies that have a pre-historic approach to software and has a seemingly unbreakable commitment to fuel sources made from dinosaurs.
When we did emerge into the wider world, prompted by work or some other unbreakable commitment, we'd remove our cell-phone batteries to make sure we weren't being tracked.
In the last few months, there were more meetings held, more hours spent, and more effort expended on reassuring Israel and its supporters of America's "unbreakable, unshakable" commitment, than in any period in our history.
He was unbreakable in his commitment to the oppressed, risked his own life and liberty to stand with them, and saw unspeakable acts of human brutality.
Cameron promised that his belief in Israel was unbreakable and his commitment to Israel's security would always be rock solid.
Signifying the change in tone between Jerusalem and Washington, Mr. Mitchell told the Israelis on Sunday that "the relationship between the United States and Israel is strong and enduring, that our commitment to Israel's security is unshakeable and unbreakable.
Again he wrote the screenplay with Bruce Willis in mind but without any commitment, and again Mr. Willis will star (reportedly he signed onto "Unbreakable" practically overnight and told Mr. Shyamalan that "it would be an honor" to appear in the movie).
Unbreakable or vulnerable?
His equanimity seems unbreakable.
This bond is unbreakable.
