It is totally possible yes. Check out Endoheic Basins Usually a lake fills up till it eventually finds a way to the ocean. If the rate of evaporation matches its ability to fill up and it can't seep to the ocean underground the only way out will be evaporation. Because all water tends to carry traces of minerals of whatever it contacts (water is a natural solvent) these tend to build up which often results in saline water. It could also just be that the rivers that drain out are so small they are too insignificant to record on your map.
Like I said, while unlikely, a giant delta is plausible. Your map does then manage to convey the landmasses bigness if it is in fact intended to be that large