You can definitely redistribute the default route from BGP into OSPF. On the router that is doing the redistribution from BGP into OSPF, use the following config and the default will be advertised in OSPF only as long as it exists in BGP.
/routing ospf instance
set [ find default=yes ] distribute-default=if-installed-as-type-1
Here is an example from our lab
[admin@IPA-LAB-OSPF-Customer] > ip route print detail
Flags: X - disabled, A - active, D - dynamic,
C - connect, S - static, r - rip, b - bgp, o - ospf, m - mme,
B - blackhole, U - unreachable, P - prohibit
0 ADo dst-address=0.0.0.0/0 gateway=100.65.0.1
gateway-status=100.65.0.1 reachable via ether5 distance=110 scope=20
target-scope=10 ospf-metric=11 ospf-type=external-type-1
1 ADC dst-address=100.65.0.0/30 pref-src=100.65.0.2 gateway=ether5
gateway-status=ether5 reachable distance=0 scope=10
[admin@IPA-LAB-OSPF-Customer] >
Logs from the BGP/OSPF router when the BGP default is withdrawn in the upstream BGP Internet peer
23:51:57 route,debug Target withdraw
23:51:57 route,debug prefix=0.0.0.0/0
23:51:57 route,debug previous attributes
23:51:57 route,debug protocol=BGP
23:51:57 route,debug scope=40
23:51:57 route,debug immediate-next-hop= address=100.64.0.1 interface=ether5
23:51:57 route,debug next-hop= address=100.64.0.1
23:51:57 route,debug origin-type=BGP
23:51:57 route,debug origin-instance-id=0
23:51:57 route,debug bgp-peer-router-id=1.1.1.2
23:51:57 route,debug bgp-peer-flags=0
23:51:57 route,debug bgp-router-id=2.2.2.2
23:51:57 route,debug bgp-origin=IGP
23:51:57 route,debug bgp-as-path=7018
23:51:57 route,debug bgp-as-path-len=1
23:51:57 route,debug bgp-nexthop=100.64.0.1
23:51:57 route,debug use-te-nexthop=yes
Same as above but as viewed from the OSPF only router
23:40:57 route,debug Target withdraw
23:40:57 route,debug prefix=0.0.0.0/0
23:40:57 route,debug previous attributes
23:40:57 route,debug protocol=OSPF
23:40:57 route,debug scope=20
23:40:57 route,debug immediate-next-hop= address=100.65.0.1 interface=ethe
r5
23:40:57 route,debug next-hop= address=100.65.0.1
23:40:57 route,debug origin-type=OSPF
23:40:57 route,debug origin-instance-id=0
23:40:57 route,debug ospf-metric=11
23:40:57 route,debug ospf-type=external-type-1
Finally, the routing table on the OSPF router after disabling it in the upstream BGP router.
[admin@IPA-LAB-OSPF-Customer] > ip route print detail
Flags: X - disabled, A - active, D - dynamic,
C - connect, S - static, r - rip, b - bgp, o - ospf, m - mme,
B - blackhole, U - unreachable, P - prohibit
0 ADC dst-address=100.65.0.0/30 pref-src=100.65.0.2 gateway=ether5
gateway-status=ether5 reachable distance=0 scope=10