Do end cities stop spawning after a certain distance?

I guess you got the rumor of a true story that got corrupted in retelling.

Everything stops generating after a certain distance. Then starts again... and stops, and starts again...

Since 1.14 a bug has been introduced to End terrain generation: MC-159283.

If you travel 370,720 blocks away from the central island, you will find yourself at the edge. All terrain generation stops - there's only void. This void surrounds the generated terrain in a ring 153,568 blocks wide - normal generation, including end cities, resumes at 524288 blocks from the central island. Then stops again at some 642,000 blocks from the center, and this continues in increasingly narrower rings.

The video by AntVenom gives more details and footage of the phenomenon.