To begin, it is always legal to request the signing of a contractual arrangement in this type of circumstance; however, it is not your duty to assent to this so long as the original tenant had the right to sublet or take on roommates. Without having signed the new lease, you (all the new tenants not on the lease) would just be tenants-at-will. This occurs when an occupant has rented a premises without a lease but pays rent at a set interval (typically monthly). The agreement for a Tenancy-at-Will may be either written or verbal. Just because a rental agreement is in writing does not make it a lease.
Either the landlord or tenant may terminate this arrangement by giving written notice 30 days or one full rental period in advance, whichever is longer. In a situation where you rented from a renter, I would want to have the assent of the landlord, as no reason is required to terminate by either party. This should be done in writing either by certified mail or have the landlord sign it, if you are presenting it in person. If rent is paid the first of each month, notice should be given prior to the first day of the month.
Many landlords are fond of tenancies-at-will because they maintain the ability to terminate a rental at any time with only a month's notice, without needing a reason. This is their prerogative for even petty reasons (e.g., they don't like your friends, or the hours you keep). This is especially true with a roommate situation, where the original lessee has a lease and is subletting rooms, because the lessor has someone on the hook for a time certain (the original lessee), but if the roommates get annoying for whatever reason to either the landlord or the lessee, you can be given a 30 day notice for a great many reasons that a lease cannot control and are not viable reasons to evict. A lease is for a duration certain, after which, the renter would either move, sign another lease, or in the case where they stayed on past the end date and continued to pay (and landlord continued to accept) rent, it would just become a tenancy-at-will.
In many ways a lease protects the renter just as much as it does the landlord, because moving is expensive and (except in very limited circumstances) the renter is guaranteed being able to keep the rental until the lease ends, so long as they pay rent and do not violate the lease or local statute(s), which would subject them to eviction. This would be beneficial in a roommate situation as it takes the power to give notice or evict away from the original lessee who sublet the rooms.
It is important to understand that just because there is a writing does not necessarily mean it is a lease. Many landlords who don't want the time constraint of a lease still like to affirm in writing basic issues like date of rent due, pets, etc. It is just cleaner than a verbal agreement.
So, in your hypothetical, the landlord could ask the new renters to (co)sign a new lease, join the existing lease, or just sign a rental agreement as a Tenant-at-Will, even though the tenancy has already begun. The renter is not obligated to sign any writing at this point. However, if the renter refuses and if the landlord insists, the landlord would likely exercise their right to terminate by serving a 30 day notice to quit. Having already taken possession, you would also be in a good position to negotiate the terms, which could be to your benefit, so it is not necessarily a bad thing.
Regarding eviction, that would only be an option to the landlord if you failed to vacate if a 30 day notice to quit was issued and you didn't move (or of course, as with any renter, if actions that would always allow the landlord the right to seek eviction occur, like failure to pay rent). I would not be concerned about showing you have a right to be there as you likely had to pay rent to move in and your check is proof that the tenancy began, and other things like having a key, etc., support your position if it ever came to that and you had paid cash. If you do ever pay cash, get a receipt.
If, hypothetically, the new renters sign a lease, I would want to make sure it is for the room and not the whole so that liability (at least for rent) is limited if others default.