First of all: Routers won't forward broadcast traffic.
From this point I'm talking about IPv4 over Ethernet, because different technologies have different ideas if something like broadcast exists or not. In this case, this also applies to WLAN, so it might be applicable to your scenario.
At first we should distinguish between two kinds of broadcast addresses: the broadcast address 255.255.255.255, and the network broadcast address which is 10.0.0.255 for 10.0.0.0/24. 10.255.255.255 is no broadcast address for 10.0.0.0/24. It doesn't even belong to the network. Actually, you even can't be sure it really is a broadcast address (It often is, though). When a client on a different network sends a packet to the address 10.0.0.255, it has no way of knowing that this address is a broadcast address. Actually, only the routers directly connected to 10.0.0.0/24 know it's the network broadcast address. Generally speaking, routers will unicast-forward incoming packets which have a network broadcast address as destination, unless they are directly connected to that network/subnet and therefore know that the destination address is a broadcast address. This is because you would be easily able to saturate all Ethernet links belonging to the destination network as switches will broadcast the packet (frame) to all ports belonging to that (layer 2) network.
Now imagine the case of 255.255.255.255. What would happen if it was happily routed? It would end up in any network that is reachable through routing. So this is an obvious exception.
The rule for the exception is: Only forward packets, that have the destination Ethernet address set to the address of the incoming interface on the router. Don't forward packets of which you know they will be a broadcast on the destination network.
A host on 10.0.0.0/24 knows that 10.0.0.255/24 will usually be the network broadcast. It will set the destination Ethernet address to the address defined as broadcast, which is all FF. This certainly isn't the address the router cares about for forwarding.
There are some mechanisms for forwarding selected broadcasts between selected networks, e.g. for spreading UPnP through collision domain borders. Those is often proxied, though.