Can a transit card move from plastic into a phone?
Where the operator supports it, yes, and what happens is a transfer rather than a copy. The balance and the entitlements move in the operator system, the plastic stops working, and the phone is provisioned with a new credential of its own.
Not a copy, by construction
A transit card is a small protected system rather than a container anyone can read, which the transport card page sets out: the balance and the history sit behind keys the operator holds, and no general purpose application obtains them.
So no phone can read a card and become it. Whatever a wallet does when it appears to absorb a card, it is doing it with the operator rather than to the card.
The tap the phone performs during such a transfer reads an identifier and whatever the card is willing to say in the open, which is enough to tell the operator which card is being presented, and nothing like enough to recreate it.
What a transfer actually does
The operator moves the account: the balance, the season ticket, the concession and the history belong to a record in its system, and that record is attached to a new credential provisioned into the phone.
That credential is issued to the device, as everything in this section is. Apple calls the resulting object a secure element pass, a pass whose data lives in the device's payment chip rather than in a file; on Android it is a service holding the operator's application identifiers.
Which is also why the transfer cannot be repeated freely between devices: each provisioning is an act by the issuer, not a file move.
What happens to the card
It stops working, and it has to. A balance that existed on both the card and the phone would be money in two places, which no stored value system can allow.
Expect the plastic to be retired at the moment of transfer rather than gradually, and expect a refundable deposit on the card, where one exists, to be handled by the operator's own rules.
Keep it until the phone has been used successfully at a real gate. A transfer that appears to have worked in an application is not the same as a barrier opening.
When it cannot be done
When the operator has not built it. This is the common case, and no amount of technical capability in the phone substitutes for the arrangement: the keys are the operator's, the account is the operator's, and the provisioning has to be agreed with the platform.
When the card is anonymous and the system has no account behind it, there may be nothing to transfer other than a balance, and some operators decline to move that.
And when the phone cannot hold the credential at all, which is the hardware and platform question the secure element page describes. A wallet that does not offer the operator's card is not hiding it in a menu.
Frequently asked questions
Can a phone read my card and become it?
No. The balance and keys are protected and belong to the operator, so a transfer is something the operator does rather than something the phone copies.
Does the plastic keep working?
No. It is retired at the transfer, because a balance that lived in two places at once would be money in two places.
Can I move it back?
That depends entirely on the operator. Treat the transfer as one way unless its own documentation says otherwise.
Why does my wallet not offer my transit card?
Because the operator has not built the arrangement with that platform. It is a commercial and technical agreement rather than a feature to enable.