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Have a look at the signal diagrams of a first order delta sigma modulator with a constant input value of 0.93 * VRef+, which is close to the upper limit of the analogue input range:

In the output data stream equally spaced pulses appear. The closer the input signal to the limit of the input range is, the lower the frequency of this residual tone is. It is obvious that the frequency easily can fall into the signal band so that it would not be filtered out by the succeding low pass filter. The amplitude of its fundamental frequency in the example above is approx. 1/14 of full scale. That means that this residual tone by far is not negligible. (93% of VRef+ corresponds to 96,5% of the full input range, i.e. 96.5% of all output bits are high and 3.5% are low.)

With an input value further away from the limit of the input range the frequency of the residual tone (and its amplitude) becomes higher. It than falls out of the transmission band and is filtered out by the succeding low pass filter.

This effect does not refer to input values close to the limits only. Have another look at the signal diagrams with a constant input value close to the center of the analogue input range (0.03 * VRef):

In this output signal a residual tone appears again. However, its amplitude is lower than before. Actually there is a sceme behind it: Input values close to 0% and 100% result in the highes residual tone amplitudes, values close to 50% in the second highest values, the next peaks are at 33.3% and 66.7%, followed by 25% and 75% and so on. Residual tones are the big disadvantage of first order delta sigma modulators. They also appear in second order modulators, but much less. And for third and higher order modulators on they may be neglected.