>>143979They either always have these things on or plug them in the day before the Sabbath. It depends on the household.
Prohibition on work is one of the strictest mitzvah. God makes it very clear to Abraham in Exodus that Jews will not work on the Sabbath. Aside from not being allowed to do their job, the literal definition of work, there's also the biblical definition. The word "work" used in the commandment to Abraham is the same that was used in God's creation of the Earth and is used immediately afterward in describing the construction of the tabernacle. This word for "work" implies creativity and domain over the world. The rabbis interpreted this as meaning any category of work which has to do with the construction of the tabernacle. This led to the 39 Melakhot, categories of creative work prohibited on the Sabbath. By the rabbis, Jews are also not allowed to touch the 6 Muktzeh, categories of tools used for creative work prohibited on the Sabbath. There are also other rabbinic prohibitions on the Sabbath, but they're more complex.
Even when employing Shabbos goy, certain rules must be followed. For example, you cannot command or hint at a command for a goy to break a Melakhot, and you can only have a goy perform something forbidden by the rabbis, such as touching a Muktzeh, if it meets certain conditions such as preventing grievous financial loss or helping the sick. However, you can hint to no subject (whine) about something which only a goy could solve by breaking a Melakhot. Saying, "Oy vey, I have only one piece of ripped toilet paper left! What ever shall I do?" would be permissible as you are not implying to anyone around you that they must break a Melakhot. You are simply despairing the situation. Whether the goy then rips the toilet paper so you may use it in your existing pile or buys more toilet paper, rips it, then adds it to your pile, is none of your concern. However, if the goy asks, "Are you saying I should do that for you?" you must always give an answer which neither affirms nor denies your desire for the action to occur, such as, "It would help," but never, "Yes." Further, you cannot apologize to or thank the goy in this situation, as that would imply you received direct benefit or were commanding the goy to break a Melakhot.
Direct benefit is defined as the ability to do something which was not previously possible after something was done to break a Melakhot or rabbinic prohibition with the intention of helping you, and the benefit of the creation of something which did not already exist. For example, you can use a newly lit room if a goy lit the room for himself and had no intention of letting you use the room before he turned off the lights. In this case of a goy lighting a room, you can ask the goy to not turn the lights off and now do activities which could not be done in the dark. However, if you ask a goy to do something which could be performed in a manner which does not break a Melakhot, yet he breaks it anyway, it is none of your concern unless he believes that you will directly benefit from his violation. If he suspects this, he cannot turn on the lights. In this case of a goy lighting a room, what you may do in the now lit room is limited to what could have been done in the dark, so you may indirectly benefit in these actions from the presence of light. This promotes lying to and tricking goyim. For example, you tell a goy that you found something of his in a now dark room. The goy goes to find his possession and turns the lights on so he may search for it. You enter the room and tell the goy to not turn the light off. The goy must now decide whether to slight you by turning light off or keep the light on despite his suspicion that you lied to him. When confronted with the lie, you say, "I thought I saw it there. Someone must have moved it." You have now confirmed that you had no intention of having the light turned on, and you have not recognized that he turned on the light. You may now do any permissible activity in that room. You cannot trick the goy into breaking a Melakhot again until he is no longer suspicious of you, but your family and friends can until he is suspicious of them as well.
There are many other rules regarding Shabbos goy. The most notable of these which I have not mentioned are the largest exceptions. The first is that during Bein HaShemashot, twilight, you can command a goy to break any Melakhot as much as you want as long as there is great need, the action is required as part of the Sabbath, or it is required for a mitzvah. The second is what may be an actual loophole and is hotly debated, the act of asking one goy to ask another goy to break a Melakhot. The first goy may decide for himself to do it for you, an action which does not benefit you because he disobeyed you. The second goy may also do the action, but he would be considered to be following the wishes of the first goy, not you.