An old style miner would only receive a stripped transaction, i.e. a transaction from which the witness has been removed. They will consider a segwit transaction to be valid but non-standard because one element remains on the stack when resolving the redeem script.
If a miner included this transaction in their block, the block would appear valid to segwit-incapable nodes, but invalid to any segwit-capable nodes as any segwit input would be missing the required witness and thus would not be properly signed. This would lead to the block being rejected by 98% of the nodes on the network, and thus the segwit-incapable miner to lose their block reward as it would not become part of the heaviest blockchain. Segwit-incapable miners can however contribute blocks that only include non-segwit transactions that build on top of the chain that includes segwit-blocks.
This means that only a miner collecting transactions with a segwit-capable node is able to create a valid block that includes segwit transactions.