Neither Pearson nor Kendall correlation really seems suited here.

It sounds like you want a regression where the dependent variable is intention to stay and the independent variable is satisfaction. This could be handled with a logistic regression, although the independent variable should probably be treated as categorical.

However, in my experience, it is is rare for such studies to be based on a single likert type question. Do you have only one?

Neither Pearson nor Kendall correlation really seems suited here.

It sounds like you want a regression where the dependent variable is intention to stay and the independent variable is satisfaction. This could be handled with a logistic regression, although the independent variable should probably be treated as categorical.

However, in my experience, it is is rare for such studies to be based on a single Likert type question. Do you have only one?