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First, there is the question of how secure your network is. It should be password protected, and the password should not be easily guessable. Some networks have several layers of password security, one restricting (for example) whether a given machine is even allowed to use the router and another restricting whether a user on an allowed machine can connect. If these passwords can be guessed by somebody, either by lucky guessing or by a brute force attack, other people can log in: for example, "Me" is a really dumb password that may be on everybody's list of things to try; so would the default password, as well as a really short password like "3W7" that anybody could discover after a few hundred attempts (since the attempts could be automated)
A good firewall will blacklist any apparent source that seems to be trying to discover a way into his machine by probing access. Some computer security products limit how much information about your machine is visible from the outside and so can reduce the chance of attack
Another issue is whether he allows other machines to control his and what password and firewall protections he has for that. People often want to be able access one of their machines from another, either in a home network or across the web: sometimes, software doesn't encrypt passwords for such transactions, and it's usually possible to allow control by other machines without any password protection at all
This is the short answer, I think: when the machine is off, nobody can be spending time trying to break into it; when the machine is on, you're probably safe if you have taken reasonable precautions; if you don't take precautions and leave the machine connected to the network always, then you're really inviting some jackass to find you and discover your weaknesses and take advantage
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