You can see Kagoshima City's countermeasures about the new coronavirus on the city's website.
If you select each language on that page, you will jump to the automatic translation page. If you check “What’s New,” you will be able to obtain some useful information. (Since it is automatic translation, it will not be 100% accurate.)
There is some useful information like: A foreign resident who has registered as a resident in Kagoshima City till April 27th of this year has the right to apply for 100,000 yen subsidy.