/32 routes received from ospf doesnt works

You mean that 10.10.10.0 belongs to these two routers, and this address cannot access the Internet? Can you explain it more clearly?? If you can share the key configuration, it will be helpful.

yes, these routers advertise /32 routes to 6720. /32 route is received but not taking priority over NULL route used for bgp to upstream provide. I hope this explains more clearly

this setup was working fine on mikrotik till i replaced it with 6720 a year back

@hashbang hello,
as you said, when the static route 10.10.10.1/32 is added, the router could reach the internet(BGP side), and if the static route is removed, the connection turns down. And I noticed that you said the OSPF route 10.10.10.1/32 does exist in the routing-table no matter the static route 10.10.10.1/32 configured or not.

Based on these information, I'm curiosity about the routing-table items when the static route configured. as you said, there will be two routes towards to the 10.10.10.1/32.

You are kindly advised to upload the corresponding configuration, I'm really confused. :)

ty,
giving you real scenario without using fake ips
this is the route received not static route added just ospf received routes
   x.86.175.9/32  O_ASE   150  20          D   x.208.153.201 Vlanif4000
now i cannot ping this ip from internet
--------------------------------------------------------------------
this is a pppoe user running on bsd pppoe-server (ospf peer)
ng0: flags=88d1<UP,POINTOPOINT,RUNNING,NOARP,SIMPLEX,MULTICAST> metric 0 mtu 1480
        inet x.208.153.201 --> x.86.175.9 netmask 0xffffffff
        inet6 fe80::1859:cd17:e802:b1fe%ng0 prefixlen 64 tentative scopeid 0x7
        nd6 options=29<PERFORMNUD,IFDISABLED,AUTO_LINKLOCAL>
i can ping from 6720
PING x.86.175.9: 56  data bytes, press CTRL_C to break
    Reply from x.86.175.9: bytes=56 Sequence=1 ttl=63 time=1 ms
    Reply from x.86.175.9: bytes=56 Sequence=2 ttl=63 time=1 ms
    Reply from x.86.175.9: bytes=56 Sequence=3 ttl=63 time=1 ms
    Reply from x.86.175.9: bytes=56 Sequence=4 ttl=63 time=1 ms
    Reply from x.86.175.9: bytes=56 Sequence=5 ttl=63 time=1 ms

but i cannot ping from internet
ping x.86.175.9
PING x.86.175.9 (x.86.175.9) 56(84) bytes of data.

now if i add x.86.175.9/32 on x.208.153.201
i'll be able to ping this user can use internet.

-----------------------------
fib information
Destination/Mask   Nexthop         Flag  TimeStamp     Interface      TunnelID
x.86.175.9/32          x.208.153.201 DGHU  t[9572573]    Vlanif4000     0x0
u can try ping from internet

Why static routes are required?
Is the default route not delivered on the S6720?

Do you mean that the 32-bit routes learned by OSPF on S6720 are advertised to the external network through BGP but cannot be accessed from the external network?
And after the static route to the 32-bit address is added to the S6720, the route is ok?
Am I right? If so, as #7 said, you may need to configure the default route or redistribute.