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I started my Google conquest to find such a game.
Searching with terms such as "The Sims Online" "Life Sim" "Browser Based life game"
to no real avail.
Then I stumbled upon a site called Tirnua, Tirnua is essentially The Sims Online, it was created by one of the developers of the Sims Online, Many users now know that The Sims Online is dead now, EA Games took it down to work on other projects.
Tirnua is very simalir to The Sims in the fact that you can create a character and customize it like a Sim, build your own house and interact with objects in it, get a job, earn money, and also interact with other players, the game is currently still in development but it's still a fun game so far.
Working in the game is different from the Sims, in the Sims your character goes off to work, somewhere in some unknown location. In Tirnua, you have to complete kind of like a puzzle, in order to collect your paycheck.
Also like the Sims you have to manage your Sims Needs, social, health and fun type needs.
To try or check out Tirnua click here.