Resources for Nedarim 18
The משנה says that סתם נדרים להחמיר ופּירושן להקל. The explanation of these words is unclear and is the subject of a מחלוקת ראשונים. תוספות and the מפרש bring a פּשט that פּירושן להקל means if at the time of the נדר a person explicitly explained what he meant (e.g. he said כבשר מליח של ע"ז) then we would believe him. However, if he didn’t explain himself at the time and only explained himself later we would not believe him. תוספות and the ר"ן both disagree with this פּשט because if that were the case then the words “פּירושן להקל” are too פּשוט and would have no חידוש whatsoever. The רדב"ז in הלכות נדרים פּרק ב הל׳ ז answers the this question by saying that the חידוש is we believe him even if he says something very unlikely (e.g. כבשר מליח of his wife who adds too much salt) we still accept it. Nonetheless, the ר"ן and תוספות have a different פּשט.They explain that פּירושן להקל means that the person can clarify what he meant weeks later and still be believed.
The פּשטות is that the ר"ן and תוספות said their פּשט whether the person made a נדר on himself where the איסור is squarely on him or whether the person made his property אסור on someone else in which case the איסור is on them. The גליון מהרש"א in the beginning of סימן ר"ח says this explicitly. What is unclear is according to the those ראשונים on what basis is the person believed weeks later? The מנחת שלמה seems to understand that it is based on עד אחד נאמן באיסורים. There are three questions on this: First, that explanation only makes sense if he is being מקיל. However, if he is being מחמיר, then it is much harder to understand how he can be מחמיר on his friend when the concept of עד אחד נאמן באיסורים only applies לקולא. In other words, if you say someone’s food is kosher they can believe you because of עד אחד נאמן באיסורים, but if you say it isn’t kosher they aren’t obligated to believe you and throw their food out (except in certain cases). So why should the ראובן have to believe שמעון that the property of שמעון was made אסור to him by שמעון’s נדר if it isn’t clear from the words? The מנחת שלמה himself asks a similar question—what if you are פּסול לעדות and have no believability for other people? Lastly, how could we give your friend מלקות if the next week you could say you meant a דבר האסור and then the נדר isn’t חל? He leaves his questions as a צ"ע. As to the first question, perhaps אין הכי נמי שמעון is not believed regarding his ראובן when he is saying something להחמיר and it is just a matter of going back to סתם נדרים להחמיר. However, this would get us into a different discussion raised by the קרן אורה (and also relevant to the third question): when we say סתם נדרים להחמיר, do you get מלקות if you violate the נדר or is it just because of ספק דאורייתא לחומרא in which case you would not get מלקות? The קרית ספר in הלכות נדרים פּרק ב הל׳ ז says that when we say סתם נדרים להחמי it is just מספק and you would not get מלקות. תוספות on דף י"ט ע"א ד"ה ור"ש says explicitly that you do get מלקות. The קרן אורה quotes the רא"ש on our דף who says the reason we assume סתם נדרים להחמיר is because if a person didn’t mean to make a נדר then they just wouldn’t have said anything. The קרן אורה assumes based on this explanation that the רא"ש holds it’s סתם נדרים להחמיר is בתורת וואדי and you get מלקות. Regarding our question, it would come out a נפקא מינה according to the קרית ספר that if you are explaining yourself weeks later לחומרא you are believed completely in regards to yourself such that you would get מלקות but only מספק regarding your friend and therefore not get מלקות.