Se compró una figura que estaba hecha de madera.
Why can't "era" be used in place of "estar"?
You could use ser/era,
Se compró una figura que era de madera.
implying a (permanent) quality of the object. You use estar + past participle to indicate the result of an action (in this case, the making process of the wood figurine). For more,you can check this other question about "Estar hecho de".
It is almost foolproof to use forms of estar (instead of ser) with a past participle (agreeing in number and gender) to describe how something appears/temporary condition. Most past participles are flexible adjectives and use forms of estar instead of ser. I tell my students that these are "fluid", "changing" or "have the ability to be changed with a force or someone's effort being applied.
The door is closed - La puerta esta cerrrada (temporary because it's not always closed. Anyone could go open it). It's a temporary condition.
I have seen and understand, however, that you can and will use forms of ser with cononocido (known) and prohibido (prohibited - though you'd likely see "se prohibe" in a se construction to say "it is prohibited") because these past participles imply descriptions that aren't fluid. They are ongoing, day to day states of being.