Cut Flowers

Tulips rarely if ever come back in their second year. If they do they arent very reliable. So they are mostly treated as annuals. Some varieties are "perennial" not many though, and they rarely if ever naturalise in the ground.

When cutting them for the vase, unless you just cut the top two inches, the stem holds the leaves, so the bulb hast got anything to replenish it...so even if it was the perennial type, its even further unlikely that it will return.
Some people will lift with the bulb intact, not only to give a longer cutting stem, but for storing, giving a staggered flowering window. Picked with the bulb, wrapped in paper, they will continue to live, once cut and put in water they will start to open.

I stopped buying tulips for the garden for this reason. Digging them in is hard work - they are very sparse in their second year. Ballerina returned for a few years - but now they are long gone. Pots possibly have better luck.

Which is why I have opted to fill the garden with daffodils- hoping they will naturalise and give me a better show as they spread.