This is unnecessary, because every user has a copy of the entire blockchain. There is no point in having half the blockchain, because what if someone tries to spend on both? Which chain is legitimate?
I think it is possible, here is an example:
Assume there are many different child blockchains.
First we mine a bitcoin and send it to address root.AAA
Then we send the bitcoin from root.AAA to child001.BBB
From the root-blockchains perspective the bitcoin is saved at child001.BBB
A lot of transactions are done in the blockchain child001 between different addresses, the root-blockchain dont care about what happens with this bitcoin as long as it is inside child001.
Now someone wants to send that coin from child001.CCC to child002.DDD, at this point the root needs to verify that the coin has not been double spent while it was inside child001, after it is verified it is sent to child002.DDD.