Got error dbus: Failed to determine seats of user "1000": Too many open files - why and how to fix?

Question

I'm running Ubuntu 16.04.6 LTS with all updates installed.

Currently I see strange behavior: I can't start new GTK applications and Qt ones.

For GTK-based applications I get:

$ atril file.pdf
Failed to get bus connection: GDBus.Error:org.freedesktop.DBus.Error.LimitsExceeded: Failed to determine seats of user "1000": Too many open files

For Qt-based applications I get:

$ konsole
QDBusConnection: session D-Bus connection created before QCoreApplication. Application may misbehave.
KUniqueApplication: Cannot find the D-Bus session server:  "Failed to determine seats of user \"1000\": Too many open files" 

KUniqueApplication: Pipe closed unexpectedly. 

I cant guess why this happens.