A similar extension existed for J1.5, but since it hadn't...
Prevent one or more user groups from changing their passwords! Enforce static passwords for selected groups.
A similar extension existed for J1.5, but since it hadn't been updated - I created a modern, compatible version.
Usage is simple - enable the plugin after selecting which user groups will be prevented from password changes. When saved, the users in those groups will not be presented with the password fields when editing their account details. Additionally, it prevents submission of passwords (just in case someone decides to submit the password field values anyway by hacking the form).