You are mixing some topics.
The TLE Format is not running out numbers (directly), the 5-digit NORAD ID is and the TLE-Format is not allowing more than 5 digits in the Satellite catalog number field (columns 3-7).
NORAD / USSF are planning to change their designator to a 9 digit number (allowing up to 999 999 999 designated objects), because more than 99 999 known objects are likely in near future.
To fit a number greater than 99 999 into the 5 digit field of a TLE (in the conversation phase), the first digit is exchanged by a letter. Every letter stands for a number. For example (i do not know the real codes) A=00XXXX, B=01XXXX, C= 02XXXX ... Z = 26XXXX. (ISS NID 25544 would be C5544). Another possible system would be, to change for NID grater 99 999 (A=10XXXX, ISS would stay 25544, object 123456 would be C3456). This would be only needed till the last subsystem is changed from TLEs to its successor. And this is called the Alpha-5 sheme.
The successor is a modified CCSDS OMM, and has no problem handling more than 9 digit numbers, as it is not saved in a fixed column stlye but in whatever computers can read (KVN, JSON, XML...). When this foramt is fully implemented in all subsystem, the alpha-5 notation can be abondoned, which will be the dead of the good old TLE.