If Router A has no route in the routing table for destination route 10.1.3.0 and we do have default route configured as---
ip route 0.0.0.0 0.0.0.0 serial0/0 on Router A
will the packets be dropped to destination route 10.1.3.0 if no ip classless command is configured on the router A.
if we configure the ip classless command in Router A config then packets will be forwarded to 10.1.3.0 network by serail 0/0?
when you say hosts at remote site you mean to say router at remote site with config as below?
when you say the corporate network it means that network for example has subnet 10.1.3.0 ?
and Remote router can not reach this subnet right?
Yes, because of the no ip classless config.
if the router is connected to major network 10/8, and does not know subnet 10.1.3.0 AND it is working in classful mode (= no ip classless) it will drop packets for the unknown subnet
if routers is NOT connected to 10/8 and does not know subnet 10.1.3.0 AND it is working in classful mode (= no ip classless) it will use the default route.
So if the router has no interface in network 10/8, it will use the default route both in classful and in classless mode
This was a concept of the past: if the router recevies packets for an unknown subnet of a connected major network, the default route was not used because old classful routing protocols do not support partitioned major networks
the modern behaviour with 12.0 is ip classless and in this case the default route is used also for unknown subnets of a connected major network because the major network could be partitioned
Hope to help