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Dmitriy Iassenev wrote:

if we try to assign

  b[nil] = {}

then we get error 'table index is invalid', but if we try

   if b[nil] == nil then

no error is raised. Is it correct behaviour?

Yes.  The manual says:

An access to an indexed variable t[i] is equivalent to a
call gettable_event(t,i).


An assignment to an indexed variable t[i] = val is
equivalent to settable_event(t,i,val).

Both of these functions are

not defined or callable in Lua.  We use [them] here only
for explanatory purposes.

Both gettable_event and settable_event use rawget to check
the current value of the table, and rawget's description

index may be any value

settable_event uses rawset to do the setting, and rawset's
description says:

index [must be] any value different from nil

See also <>.