If that's all that's going on, there's not likely to be a problem. Traffic for the piggy system is accepted and passed on (both directions) by the neighboring system.
However, if the piggy system is attempting to run software on the neighbor system (for good purposes (are there any?) or bad (lots of those)) most any kind of damage to neighbor's system (software or data) is possible if the attempt succeeds, but that has nothing to do with wireless particularly. That sort of possible vulnerability is also possible with wired networking as well. And, for that matter, with sneakernet sharing of thumbdrives and floppies. the underlying problem is really a human one, not a technological one. Poorly designed technology (eg, the WEP security standard) merely facilitates human misbehavior.
The legal question is not entirely clear. Using neighbor's network connection may be held illegal if it comes up, and use of it for illegal purposes (eg, child porn distribution, or terrorist planning, is certainly criminally chargeable, but these would be illegal even wireless weren't involved at all). Prosecutors have construed use of neighbor's open and unprotected wireless access point as a break in to an access controlled computer system -- like getting a password username combination to a bank's computer -- even though the standard specifically sets up open access points to offer connections to all comers. And they have sometimes claimed that piggy is stealing service (like electrical power or something similar) even though neighbor is not selling it or offering it for sale to anyone.
Access to neighbor's system is possible (usually) only if neighbor doesn't bother to properly configure the access point; this lck of configuration may be due to ignorance, or a deliberate decision not to bother with any configuration after the new network stuff finally begins to work, or ... The situation is less confused if the neighbor was asked and refuses permission, or if piggy breaks into the WiFi network after neighbor actually tried to configure his radio to prevent others' use. And if it comes to the neighbor's attention that piggy has been distributing child porn, and the neighbor does nothing to block access raises the possiblity that some prosecutor might try to charge neighbor as a conspirator when they pick up piggy.