While most plants cannot survive in salt water, there are plants that can.
One example of a type of plant that can survive in salt water is something called a marine seagrass. I have attached a link here to a page that talks in depth about this kind of plant.
Another example of a plant that grows in salt water is the mangrove. Mangroves grow along the coasts of many tropical places, including the island where I grew up. Their roots go down into the floor of the ocean right along shore. The "wettropics.gov" site I have linked to gives more information about these plants.
In general, though, plants cannot live in salt water because they do not have genes that allow them to tolerate salt. Mangroves and marine seagrasses do have such genes.
There are special types of plants growing in saline soil or saline water with preponderance of salts in it. These are known as mangrove. Such plants show some special characteristics. Mangrove plants produce a large number of stilt roots from the main stem and the branches. In several cases, in addition to the stilt roots, special roots called respiratory roots or pneumatophores are also produced in large numbers. They develop from underground roots, and projecting beyond the water level look like so many conical spikes distributed all around the trunk of the tree. In some places they grow so thickly that passage through them is difficult. they are provided with numerous pores or respiratory spaces in the upper part, through which exchange of gases for respiration takes place.
Plants cannot grow normally in salt water as the salt in the water interferes with the balance of the salt and water contained in the plant and can damage the plants. Some plants that grow in saltwater use different techniques to protect themselves and get rid of the extra salt. These include the presence of membranes that reduce the amount of salt absorbed. Others store the excess salt in leaves and these leaves regularly drop off, ridding the plant of the salt. Some plants have very dense roots which help it in combating the effect of saltwater that drains the water in the plants.