So I went through the last big crash with my consulting company and we never reduced our contracted rate to try and save a gig, but we did other things. My suggestion here would be to reach out and just tell whomever is managing your contract that you recognize we are in trying times and that you are there to help and if there is anything you can do that might help them keep the level of support or increase it you are happy to discuss it. What you have to remember is most of the time they will cut a FTE before they cut a contractor in a time like this because you are cheaper then their loaded FTE's likely. There are exceptions to when that isn't true of course, but in general contracting gets better during downturns not worse. When there is uncertainty in the market companies still have demand and need people but they are cautious to bring on FTE's so instead they hire out to contractor at market rates.
If they reach out to you, always start it with you are willing to give them an extra 5-10 hours (depending on how much time you are doing) for a period of time to help through this without billing for it (you will put it on every invoice but show it as good will). Yes, effectively it is the same thing as lowering your rate to a degree, but it doesn't lower your contracted rate. Lowering your rate for an existing client is always the absolute last ditch effort, because it sends the wrong message to them and it will generally hurt you in the longer term, at least with medium to large businesses. If you are working with a small business or startup the opposite is fair, lowering your rate a bit will help them.
My goto was always to offer them a bit more time, or offer to give them a higher monthly discount for paying timely during this time. e.g. it solves two issues, you get paid timely while keeping your gig and they get a break on costs. If you haven't been through this before, the thing that typically happens is companies will sit on invoices longer during tough times, especially for existing small vendors, so a discount is a way to help incentivize them to pay on time but give them a break someone else may not.
Your other option is to offer them fewer hours which means lower cost but lets you open yourself up to finding other gigs, but I'd work to avoid lowering your rate. One other point, if this is a larger company they will want to formalize any rate change in a contract adjustment, which once you open that up and it goes to legal it could open a whole can of worms, so avoid it and use discounts, increased offerings and/or total billable hours to adjust best you can.