A more appropriate reference is NIST Special Publication 800-90B, "Recommendation for the Entropy
Sources Used for Random Bit
Generation" since you're using the term "true random number generators" and not "deterministic".
There's too much for this answer, so I refer you to §3.1.5.
What if the true rng supplied only 1s very rarely
Irrelevant, and very common in ring oscillator entropy sources. Let's say "rarely" means one transition in a 100 samples. You throw away 99 samples, and just keep the 100th through a process called decimation. I seen divide by 512 decimators in experimental ring oscillators. E.g.:-
NIST keep changing the entropy estimation procedures (to discourage their use?) but the latest is §3.1.5.1.2 Entropy Assessment using Vetted Conditioning Components reproduced here:-
This is NIST's version of the Left Over Hash lemma (inferred from above step 4). Although many designs simply use the original lemma when no cryptographic conditioning components are necessary. And the advantage of the lemma is that it allows direct computation of the final entropy bias.
So in summary, entropy source bias is easily dealt with by well established techniques. Of course the more bias, the slower the final output rate/less efficient design.