My postdoc advisor just now said she cannot support me after 6 months. What should I do? After graduating in February, I was waiting for my work permit to start my one-year postdoc position. Finally, after 2 months delay (due to COVID-19), I have got my permit today and now I can start the paperwork to have my position finalized. However, now my postdoc advisor informed me that there's a change in the financial situation due to an industrial funding partner retracting their contribution and I can be supported for only 6 months. So, now I am clueless on what to do about this.

What should I do? I am going to start applying to positions again from next week. Any other advice for me?
Given that your contract wasn't finalized, there probably isn't much you can do. 

But there are a couple of options, all risky. You could ask the PI if there is any chance that additional funding could happen to at least complete a year. The answer might be maybe and you could decide to take a risk and do the short postdoc and hope for more. In fact, you could ask to be first in line for additional funding. You might actually be able to help secure funding as part of your work. 

You could also, just drop out of the position and search for something better, provided that you have some way to make that work. 

But looking for another position immediately is certainly a smart thing to do.