Why is the session on a subdomain overwritten when entering the main domain?

Question

Sessions

We have 3
example.com
domains a.example.com
b.example.com
Each domain uses a common cross-domain session:

session_set_cookie_params(604800, '/', '.example.com');

Everything worked great. Until we moved to a new server (all 3 sites moved together to the same server).
Cookies are set fine, but sessions behave strangely. We log in to a.example.com and do not go to another domain yet, everything is OK, but as soon as we go to example.com or b.example.com, the content of the session is cleared, but the cookie remains unchanged (set for the .example.com domain) .
What in the settings of Apache or PHP can lead to such behavior?