You have to start searching for a new job as soon as you know you will be unemployed. In my case (when I was between studies and my first job), they requested 10 documented applications per month if I remember correctly, which could be less if/when I was partially employed, down to a minimum of 3).
In my experience, they are not very qualified to help people with specialized skills so they’d mainly rely on you to do your searches and aim at jobs that you are qualified for. They wouldn’t come to you with situations like “hey, we’ve got this great position you should apply for!” that they would then force you to accept. Of course, with time, there are less and less relevant positions/companies where we can apply so you’ll have to think of a backup plan with time. It’s possible to send applications hoping not to be hired but it can backfire and you may end up being hired anyway (some companies have very poor HR departments) so you’d have to be prepared for that situation.
It is but they won’t offer/pay for just anything, you’d have to justify that the relevant knowledge/skill does help your employability and even then, I would guess many kinds of training would not pass the test.
For more accurate information regarding the legalities/procedures in regards to unemployment: Unemployment in Switzerland