Standard rental insurance and landlord insurance policies do not cover lease breaks. The only situation where either the tenant or the landlord would be protected against monetary loss in the event of a broken lease would be if one of you acquired a more specific policy designed to protect against lease breaks.
Lease breaks and renters' insurance
Tenants should definitely have renters' insurance, but only because it will protect against loss or theft of personal belongings, personal liabilities, medical payments to others or loss of use (like if there's a fire and you can't stay in your place anymore). It's not designed to protect against the eventuality that a renter changes jobs or relationships and needs to break their lease.
Lease break insurance for landlords
Insurance companies generally don't like to offer policies that payout business owners in the event that their core business isn't going well. If you're a landlord, keeping your units occupied is your core business. This is why you can't easily get a policy that covers sudden vacancy and the lost rent that comes with it.
Landlord insurance should have something called loss of rent coverage, but that is only intended to cover a landlord against externalities that led to lost rent, like hurricanes. It's similar to the loss of use coverage that renters can expect from their policy.
Landlords can, however, get special anti-vacancy policies that cover lost rent due to surprise vacancy losses. These policies are the institutional version of a personal guarantor. They fall outside the scope of standard landlord insurance policies so renters shouldn't assume that their landlord has one and, depending on the market, it may be more common for the tenant to pay the monthly fees rather than the landlord.
The information provided on this website does not, and is not intended to, constitute legal advice.