**Edit:** According to the comment of Andre Henriques I revise the question:

What is  an example  of  a  noncommutative unital $C^\star$  algebra $A$, which is not Morita equivalent to a  commutative algebra,  such that for  all unital subalgebra $B$ of  $A$, $ K_{0}(B)$  has $\mathbb{Z}$ as a summand? This  question is  motivated by [this post](https://mathoverflow.net/questions/169270/topological-k-theory-for-commutative-c-algebras) and the fact that  commutative  algebras and their  matrix algebras satisfies the  above  property.