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This value is zero, and you can set that regardless of what's actually in the GDT.

I don't recall it documented this way (the NULL descriptor may contain anything). Is it really so?

Null Selector. Null selectors have a selector index of 0 and TI=0, corresponding to the first entry in the GDT. However, null selectors do not reference the first GDT entry but are instead used to invalidate unused segment registers. A general-protection exception (#GP) occurs if a reference is made to use a segment register containing a null selector in non-64-bit mode. By initializing unused segment registers with null selectors software can trap references to unused segments.

The first entry of the GDT is not used by the processor. A segment selector that points to this entry of the GDT (that is, a segment selector with an index of 0 and the TI flag set to 0) is used as a “null segment selector.” The processor does not generate an exception when a segment register (other than the CS or SS registers) is loaded with a null selector. It does, however, generate an exception when a segment register holding a null selector is used to access memory. A null selector can be used to initialize unused segment registers. Loading the CS or SS register with a null segment selector causes a general-protection exception (#GP) to be generated.

In practice, there's a hack in the wild that repurposes the 0th GDT entry as the size-offset pair used for LGDT (to save 6 bytes of bootloader space) with no known ill effects other than relying on undocumented behaviour - when that documentation was still lacking. The idea is that the CPU does not need to access the GDT in memory if there are 8 bytes of zeroes there "by definition"

A descriptor table is simply a memory array of 8-byte entries that contain
descriptors, as Figure 5-5 shows. A descriptor table is variable in length
and may contain up to 8192 (2^(13)) descriptors. The first entry of the GDT
(INDEX=0) is not used by the processor, however.