To start from the beginning, there is a liability exposure that even
volunteer board members have. In many cases, the association, or even
specific members of the association, can be sued for neglegent acts of
all kinds. The insurance that covers board members falls under
"Executive Insurance" coverages. These include Directors and Officers
(D&O), Errors and Omissions (E&O), and Employers' Practices and
Liabilities (EPLI). You can purchase these coverages together (as is
the case most of the time) or separately. These coverages provide
specific coverage to guard against the personal assets of board
members. It is most definitely the case that without this coverage,
board members' assets are at risk.
As far as events go, if we are talking about a homeowners' association
where events are held on common grounds owned by the association then
the association is liable for injuries during sponsored events (or
otherwise). If the association is not specifically a homeowners'
association, then the same liability could apply depending on where
the events are held. The truth is, no matter who owns the property at
which events are taking place, the association could be sued if they
sponsor an event at which something unconciounable happens. To cover
these events, many commercial insurance companies offer specific
coverages for various types of associations. The coverages are
inexpensive and can protect individual board members' liability.
I am an insurance agent, and out agency writes only 3 homeowners'
associations, and the annual premiums (including executive coverages)
is less than $2,000 a year.