Anonymizing Proxy Server Question

Take this picture:

LAN<->ROUTER<->MODEM<->[POSSIBLE-FIREWALL]<-> External-Destination

Suppose the LAN is, say, somewhere in China and
the desired External-Destination is disallowed
by the PRC.

A paper I have been reading suggests that it is
possible to insert a proxy server to the left
of the MODEM in the picture and, yet, have
the traffic to the External-Destination be
invisible to a firewall inserted by the PRC after
the MODEM.

If all traffic that leaves the MODEM has to go through
the PRC firewall then I can't see anyway it can
get to the destination. Moreover, I can't see
any way the attempt can be anonymized since the
MODEM identifies the sender.

I can see that a proxy inserted after the firewall
can work. That might be the case if that source
in China has friend/family in the US, for example,
who is willing to forward all traffic coming
from China.

Am I missing something?