Suddenly, my Ubuntu virtual machine in VirtualBox stuck at initializing screen (just before login). How to deal with this?

There can be a lot of causes for this. But one of the most common problem is insufficient video memory allocated for a virtual machine.
How can we check if this is our issue? Let’s check the error log in our virtual machine.
1. Shutdown your virtual machine if it is powered on.
2. Start it again by holding the SHIFT key while the virtual machine is started. This step can be a little clumsy and my suggestion is to close as many windows as you can. You should be careful that the focus is on the virtual machine window before pressing a SHIFT key. Maybe you will have to try this several times to be successful.
3. If you success a GRUB menu will be shown:

4. Select  Advanced options for Ubuntu and on next screen select Ubuntu, with Linux x.x.x.x-generic (recovery mode) and Resume on Recovery Menu. 
5. After system loading, the Ubuntu login will appear. Log in and search for Log application and check records in system logs. Of course,  you can use Terminal and Journalctl if you are familiar with geek’s approach. 
If you see something like this:
[drm:drm_crtc_helper_set_config [drm_kms_helper]] *ERROR* failed to set mode on [CRTC:29:crtc-0]

then you can try our solution.
1. Shutdown your virtual machine.

2. Open Setting for that virtual machine in VirtualBox Manager and choose Display on the left.
3. Increase Video Memory to at least 80 MB.

Now start your virtual machine again … and with a little luck, your Ubuntu will work again.