Can extensions methods be called on no object?

Is this allowed to work or just a bug?

The code after you've edited the question (to call s0.TestNull() instead of null.TestNull() is meant to work, yes.

Extension methods are just syntactic sugar for calling static methods as if they're instance methods. So a call of:

s0.TestNull()

is converted into

ClassContainingExtensionMethod.TestNull(s0)

... and that's all. No nullity checks are performed automatically.

This can actually be really useful - imagine if string.IsNullOrEmpty had been an extension method - then instead of writing:

if (string.IsNullOrEmpty(foo))

you could write the more readable:

if (foo.IsNullOrEmpty())

However, this power should not be taken lightly - most extension methods should throw ArgumentNullException if the first parameter has a null value, and those which don't should be very clear about it. (It should be relatively rare for such a method not to include Null somewhere in the name.)