That can be managed with the split/merge policy.
I believe that domains would be required to enable this functionality.
take a look at the split policy in the domain section of help
An attribute for any given table, feature class, or subtype can have
one of three split policies that control the value of an attribute in
the output object:
Default value—The attributes of the two resulting features take on the default value for the attribute of the given feature class or subtype.
Duplicate—The attribute of the two resulting features takes on a copy of the original object's attribute value.
Geometry ratio—The attributes of resulting features are a ratio of the
original feature's value. The ratio is based on the ratio in which the
original geometry is divided. If the geometry is divided equally, each
new feature's attribute gets one-half of the value of the original
object's attribute. Geometry ratio policies only apply to domains for
numeric field types.
In the parcel example above, when a parcel is split, the Area
attribute is automatically assigned as a property of the resulting
geometry. The value for Owner is copied to the new objects (in this
database, splitting a parcel does not affect its ownership). The
PropertyTax is calculated based on the area, or size, of a parcel. To
calculate the PropertyTax for each of the new objects, the split
policy divides the PropertyTax of the original parcel proportionally
among the new features according to their area.
If you do much topology you should already be aware of the topology rules.
they can be found here topology poster
topology help is here