As soon as a living organism dies, it stops taking in new carbon.The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but the carbon-14 decays and is not replaced.However, the principle of carbon-14 dating applies to other isotopes as well.
Once the tree dies, it ceases to take in new carbon, and any C-14 present begins to decay.
Other useful radioisotopes for radioactive dating include Uranium -235 (half-life = 704 million years), Uranium -238 (half-life = 4.5 billion years), Thorium-232 (half-life = 14 billion years) and Rubidium-87 (half-life = 49 billion years).
The use of various radioisotopes allows the dating of biological and geological samples with a high degree of accuracy.
However, radioisotope dating may not work so well in the future.
Anything that dies after the 1940s, when Nuclear bombs, nuclear reactors and open-air nuclear tests started changing things, will be harder to date precisely.