I think I have figured out the problem.
It is a Dashboard plugin.
I've debugged the password encoding process, and found, that after registration, users password was encoded two times. First time, hash code was correct, but after second time it was messed up.
There is a Call Stacks for encryption:
First time:
/framework/security/PasswordEncryptor.php.PasswordEncryptor_Blowfish->encrypt : lineno 179() /framework/security/PasswordEncryptor.php at line 179
/framework/security/Security.php.Security::encrypt_password : lineno 830() /framework/security/Security.php at line 830
/framework/security/Member.php.Member->onBeforeWrite : lineno 728() /framework/security/Member.php at line 728
/framework/model/DataObject.php.DataObject->write : lineno 1058() /framework/model/DataObject.php at line 1058
/mysite/code/PageRegistration.php.PageRegistration_Controller->doRegister : lineno 62() /mysite/code/PageRegistration.php at line 62
/framework/forms/Form.php.Form->httpSubmission : lineno 360() /framework/forms/Form.php at line 360
/framework/control/RequestHandler.php.RequestHandler->handleRequest : lineno 184() /framework/control/RequestHandler.php at line 184
/framework/control/RequestHandler.php.RequestHandler->handleRequest : lineno 204() /framework/control/RequestHandler.php at line 204
/framework/control/Controller.php.Controller->handleRequest : lineno 153() /framework/control/Controller.php at line 153
/cms/code/controllers/ContentController.php.ContentController->handleRequest : lineno 197() /cms/code/controllers/ContentController.php at line 197
/cms/code/controllers/ContentController.php.ContentController->handleRequest : lineno 180() /cms/code/controllers/ContentController.php at line 180
/cms/code/controllers/ModelAsController.php.ModelAsController->handleRequest : lineno 68() /cms/code/controllers/ModelAsController.php at line 68
/framework/control/Director.php.Director::handleRequest : lineno 307() /framework/control/Director.php at line 307
/framework/control/Director.php.Director::direct : lineno 119() /framework/control/Director.php at line 119
/framework/main.php.require_once : lineno 126() /framework/main.php at line 126
/index.php.{main} : lineno 66() /index.php at line 66
Second time:
/framework/security/PasswordEncryptor.php.PasswordEncryptor_Blowfish->encrypt : lineno 179() /framework/security/PasswordEncryptor.php at line 179
/framework/security/Security.php.Security::encrypt_password : lineno 830() /framework/security/Security.php at line 830
/framework/security/Member.php.Member->onBeforeWrite : lineno 728() /framework/security/Member.php at line 728
/framework/model/DataObject.php.DataObject->write : lineno 1058() /framework/model/DataObject.php at line 1058
/dashboard/code/DashboardMember.php.DashboardMember->onAfterWrite : lineno 49() /dashboard/code/DashboardMember.php at line 49
/framework/core/Object.php.Object->extend : lineno 913() /framework/core/Object.php at line 913
/framework/model/DataObject.php.DataObject->onAfterWrite : lineno 949() /framework/model/DataObject.php at line 949
/framework/security/Member.php.Member->onAfterWrite : lineno 755() /framework/security/Member.php at line 755
/framework/model/DataObject.php.DataObject->write : lineno 1175() /framework/model/DataObject.php at line 1175
/mysite/code/PageRegistration.php.PageRegistration_Controller->doRegister : lineno 62() /mysite/code/PageRegistration.php at line 62
/framework/forms/Form.php.Form->httpSubmission : lineno 360() /framework/forms/Form.php at line 360
/framework/control/RequestHandler.php.RequestHandler->handleRequest : lineno 184() /framework/control/RequestHandler.php at line 184
/framework/control/RequestHandler.php.RequestHandler->handleRequest : lineno 204() /framework/control/RequestHandler.php at line 204
/framework/control/Controller.php.Controller->handleRequest : lineno 153() /framework/control/Controller.php at line 153
/cms/code/controllers/ContentController.php.ContentController->handleRequest : lineno 197() /cms/code/controllers/ContentController.php at line 197
/cms/code/controllers/ContentController.php.ContentController->handleRequest : lineno 180() /cms/code/controllers/ContentController.php at line 180
/cms/code/controllers/ModelAsController.php.ModelAsController->handleRequest : lineno 68() /cms/code/controllers/ModelAsController.php at line 68
/framework/control/Director.php.Director::handleRequest : lineno 307() /framework/control/Director.php at line 307
/framework/control/Director.php.Director::direct : lineno 119() /framework/control/Director.php at line 119
/framework/main.php.require_once : lineno 126() /framework/main.php at line 126
/index.php.{main} : lineno 66() /index.php at line 66