Williams deputy team boss Claire Williams says she fears Formula 1 could lose "an awful lot" of teams due to the coronavirus.

Currently, all operations are on a prolonged shutdown in this extended period without races, while a range of cost-cutting and saving measures have been suggested with some agreed.

Even so, with the revenue generated by F1 the lifeblood of some teams, Williams says the longer the current situation goes on, the more teams will be at risk.

"It is scary that we could lose not just one or two teams, but an awful lot of teams if we don't get back racing," she said, speaking to Sky Sports.

"The financial model that we have in our sport means that we are all so reliant upon the money that we receive from the results that we get in the constructors' championship.

"You take that away, and coupled with the fact that sponsorship isn't at the level that it is in Formula 1 at the moment and in sports in general, that makes trying to find a budget to go racing really incredibly difficult."

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A lot of emphasis currently is on the response by F1 owners Liberty Media, who have already forwarded prize money payments to some teams to try and help them through the crisis.

However, F1 CEO Chase Carey is also now warning that stakeholders shouldn't depend on the commercial rights holder to bail them out.

"Whether it's the teams, or promoters or sponsors, we're not going to be handing out candy to everybody," he said on a conference call with investors last week.

"We're going to expect to be treated fairly, but we're going to deal with it as adults, and with the expectation that 2021 is going to look like the business that we all knew four months ago."

As for the prize money for this season that is so critical for teams like Williams, Carey also signalled the pot would not be boosted beyond what is required.

"The prize fund is a contractual formula, so the prize fund is what it is," he said.

"Realistically we couldn't unilaterally change it if we choose. To expand on that, it's a percentage of profits, and profits will be down, and the prize fund would be down.

"Would we do something to support certain teams? We're not in the business of handouts, but that being said we'll engage with all our partners and figure out how do we go forward in a way that makes sense for everybody.

"I don't think we really move to the next level until we really know what that is. Obviously we have a lot of moving parts, we haven't settled the calendar, we don't know how many races have fans," the American added.

"At this point, we have a wide range of outcomes on the ultimate prize fund. I think when we have a better handle on that we'll see where we are and see if it's appropriate or right for us to do anything, whether it's with a team or with any of our other partners."

A key way F1 hopes to boost that prize fund is by reaching the 15 races needed to secure full payments from TV broadcasters.

But, while it is still hoped that can happen by starting the season in Austria in July, Williams says she won't risk her staff, even if it risks her team.

"You have to weigh up the need to go back racing in order to ensure sure your team's survival against the very important reality of ensuring your people remain safe," Williams said.

"For me, at the end of the day, my people are always going to win out.

"I certainly hope that doesn't cost us our team, but the safety of our people, whether that be returning them to work at Grove or asking them to travel, is going to be absolutely paramount.

"We will certainly not be sending people back racing until it is appropriate to do so.