Asbestos liner is used in a casting ring to:
With the use of solid metal rings or casting flasks, provision must be made to permit investment expansion. The mold may actually become smaller rather than larger because of the reverse pressure resulting from the confinement of the setting expansion. This effect can be overcome by using a split ring or flexible rubber ring that permits the setting expansion of the investment.
However, the most commonly used technique to provide investment expansion is to line the walls of the ring with a ring liner. Traditionally, asbestos was the material of choice, but it can no longer be used because its carcinogenic potential makes it a biohazard. 
Two types of nonasbestos ring liner materials have been produced: an aluminosilicate ceramic liner and a cellulose (paper) liner.
To ensure uniform expansion, the clinician or technician cuts the liner to fit the inside diameter of the casting ring with no overlap.
Reference: PHILLIPS’ SCIENCE OF DENTAL MATERIALS, 12th ed page no 215
Facilitate venting of the mold
Retard the heating of the investment
Permit expansion of the mold
All the above