SYSOBJECTS table has an identity column of int type. But values in ID column are getting close to int max value. I guess it'll become impossible to create any objects when it reaches its maximum.
Is there a way to alter that table to convert ID column to BIGINT for example? Or are there any tools that can solve this problem?
you have nothing to worry about.
Object ids are not assigned sequentially. They have a gap of 16000057 between each one and just wrap around on overflow (approx every few hundred object creations) so it is normal you will see some big numbers in there.