Can an indicator be NULL?

Can an indicator be NULL?

An attribute that is defined as an indicator has only two values, such as Active/Inactive, Yes/No, True/False, and On/Off. I was asked during a training class this week if NULL (empty) can also be a value. Can an indicator attribute have three values, such as Active, Inactive, and NULL? That is, can an indicator attribute be optional? If an indicator attribute value is always required, than only two values are possible (e.g. Active/Inactive) and a NULL value, if it occurs, will be replaced with a default value (such as Active).

Which do you think is better and why, an indicator attribute that is defined as NOT NULL and uses a default value, or an attribute that is defined as NULL and allows the attribute to be optional?