What happens if someone with a permanent contract in Austria gets fired in the first ten months? I've heard that it requires one year to mature the contribution for unemployment benefits.
Your information seems correct (click on “Wer?”). The relevant part is:
Eine gewisse Mindestdauer arbeitslosenversicherungspflichtiger Beschäftigung muss jedenfalls nachgewiesen werden und die Bezugsdauer darf nicht erschöpft sein.
Die Mindestbeschäftigungsdauer für den Erwerb eines Anspruches beträgt:
bei erstmaliger Inanspruchnahme einer Leistung nach dem Arbeitslosenversicherungsgesetz 52 Wochen an arbeitslosenversicherungspflichtiger Beschäftigung innerhalb der letzten 2 Jahre vor der Geltendmachung des Anspruches,
bei weiteren Inanspruchnahmen des Arbeitslosengeldes 28 Wochen an arbeitslosenversicherungspflichtiger Beschäftigung innerhalb des letzten Jahres vor der Geltendmachung des Anspruches.
A certain minimum duration in an activity covered by mandatory unemployment insurance should in any case be documented and the benefit duration should not be exhausted
The minimum activity duration to claim a benefit is: for the first request, 52 weeks within the 2 years before the claim,
For any subsequent request 28 weeks in an activity covered by mandatory unemployment insurance in the year preceding the claim.
What happens if you lose your job without fulfilling the requirements for unemployment benefits in Austria is, basically, nothing. These benefits are designed like an insurance and from the perspective of the unemployment insurance system, you simply aren't covered. It would be the same if you exhausted your benefits.
Many European countries have some sort of general welfare benefits (typically lower than unemployment benefits) unrelated to previous employment to alleviate poverty (in Austria, it's called Sozialhilfe). This would automatically “catch” locals who fall out of the unemployment benefit system but is not logically related (and, indeed, in Autria it's administered completely separately on a provincial level). However, it might not necessarily apply to non-citizens.
EU citizens should also have access to these benefits on a par with citizens if they lived at least 5 years in the country but before that the rules are more complex and countries are able to set restrictions.
There is one important additional detail to this. It is true that you must have been employed for a year within the last two years to qualify for unemployment support, but this employment doesn't have to be in Austria only. Employment within another EU country is also counted in, you just need to request a U2 form from that other country and submit it to AMS in Austria.