During this time the belly of the oyster gets very soft and creamy. Visible lines, or tracks, appear on the belly. Finally, after spawning, the oyster becomes very watery and clear without much texture or flavor. No, that is just their condition. Whether you want to eat them or not is up to you.
Some people prefer an oyster slightly watery.
I call this a French style oyster. Because the oyster beds in France are so overcrowded, French oysters tend to be thinner, less full. European chefs tend to prefer this style of oyster and will think an oyster is out of season if you send them a plump, fat oyster. Asian and American chefs tend to prefer an oyster that fills the shell with fatness and have no use for thin oysters. It's just a matter of preference.