After a restart due to a system crash the ethernet interface is disappeared. How to restore it?

Solved myself. Maybe it can help someone else:

1) I discovered that Ubuntu 19.10 by default is not defining the network interfaces by the /etc/network/interfaces file. This file doesn't exist. To manage the network interfaces it is using the network manager: http://manpages.ubuntu.com/manpages/cosmic/man1/nmcli.1.html

2) First of all I list the interfaces by this command: sudo nmcli device show

[sudo] password di developer: 
GENERAL.DEVICE:                         ens33
GENERAL.TYPE:                           ethernet
GENERAL.HWADDR:                         00:50:56:3A:4B:1E
GENERAL.MTU:                            1500
GENERAL.STATE:                          10 (non gestito)
GENERAL.CONNECTION:                     --
GENERAL.CON-PATH:                       --
WIRED-PROPERTIES.CARRIER:               off
IP4.GATEWAY:                            --
IP6.GATEWAY:                            --

GENERAL.DEVICE:                         lo
GENERAL.TYPE:                           loopback
GENERAL.HWADDR:                         00:00:00:00:00:00
GENERAL.MTU:                            65536
GENERAL.STATE:                          10 (non gestito)
GENERAL.CONNECTION:                     --
GENERAL.CON-PATH:                       --
IP4.ADDRESS[1]:                         127.0.0.1/8
IP4.GATEWAY:                            --
IP6.ADDRESS[1]:                         ::1/128
IP6.GATEWAY:                            --
IP6.ROUTE[1]:                           dst = ::1/128, nh = ::, mt = 256

As you can see the ethernet network interface neamed ens33 is at the moment not handled (in italian "non gestito"), so at the moment is disabled.

3) I enabled it by

nmcli networking on

now it works fine

Here is what fixed the same problem for me (AndreaNoboli's answer sadly didn't help):

check /etc/NetworkManager/NetworkManager.conf and /etc/NetworkManager/conf.d/ to see if there's a managed=false entry which could be changed.

I got it from an only tangentially related issue elsewhere: https://access.redhat.com/discussions/6278791, but it worked perfectly for me.